A magical beast can be awakened using Dragon magazine material…
The 9th-level Drd spell awaken magical beast [trans] (Dragon #304 38) is like "awaken, but [the caster] awaken[s] a magical beast with an Intelligence score of no higher than 3 [like a hippogriff (Monster Manual 152)]. Like an awakened animal, the magical beast gains 3d6 Intelligence, +1d3 Charisma, and +2 hit dice" (links added). The spell costs the caster 500 XP, twice the XP cost of the awaken spell.
The spell dates to before the 3.5 revision but was never updated therefore it's game-legal yet subject to minor adjustments by the DM (see Dungeon Master's Guide 4). I suspect that many DMs who would allow the spell awaken magical beast into their campaigns would simply have it align with the 3.5 revision of the 5th-level Drd spell awaken [trans] (Player's Handbook 202) but keep its higher spell level and XP cost. (In fact, a DM could probably reduce its spell level by 1–3 and not have the spell break anything, but I've not tried that.)
…But there's a less expensive albeit more fragile way to grant a magical beast a higher Intelligence score
If the goal is to uplift to humanlike sentience a magical beast that possesses an Intelligence score of 1 or 2 sooner than with a 9th-level spell, the easiest way is to plop on its noggin a headband of intellect +2 (Dungeon Master's Guide 258) (4,000 gp; 0 lbs.). That is, the awaken spell "awaken[s] a tree or animal to humanlike sentience," and humanlike sentience apparently includes a rolled Intelligence score of 3d6, making even 3 a high enough Intelligence score… according to the spell awaken, anyway.
(To be clear, a creature must already have a Charisma score to be a creature at all: "Anything that lacks… Charisma is an object, not a creature…" (Monster Manual 298), so that's not a factor for humanlike sentience for a magical beast, and neither is, so far as I can tell, the extra Hit Dice that the awaken spell grants. Also, so you know, the tree and sponge exception (ibid.) makes some objects living but still not creatures.)
The DM must determine what happens when the creature that possesses an Intelligence score of 1 or 2 dons or removes the headband, though. For instance, on Intelligence, in part, says, "Any creature with an Intelligence score of 3 or higher understands at least one language (Common, unless noted otherwise)" (MM 7) therefore the creature may be able to understand Common while it wears the headband. And on Advancement says, "Often, intelligent creatures advance by gaining a level in a character class instead of just gaining a new Hit Die" (ibid.). How intelligent? The DMG says, "[D]on’t allow players to play creatures who have an Intelligence score of 2 or lower" (172), so probably that intelligent (although a DM could rule otherwise).
In other words, a hippogriff that wears a headband of intellect +2 that gains fighter class levels and can understand Common may not be able to gain further class levels or be able to understand Common if the headband is removed. (In addition to any other effects, obviously.)
The question proposes a process that, as written, won't work
The 1st-level spell aspect of the wolf [trans] (Spell Compendium 16–17) has a range entry of personal. On Creating Potions says, "Spells with a range of personal cannot be made into potions, so spells such as shield [and aspect of the wolf] never exist in potion form" (Dungeon Master's Guide 286 and link mine). Nonetheless, for example, a DM may allow Gremma's cauldron (Expedition to Undermountain 217) (5,000 gp; 0 lbs.) to transform a scroll of aspect of the wolf (1st-level spell at caster level 1) (25 gp; 0 lbs.) into a potion of aspect of the wolf by having the cauldron's user expend the scroll, expend 25 gp in raw materials, and spend 1 XP. (Other ways to affect a creature other than the caster with the spell aspect of the wolf also exist; this is just among the easiest.)
On Casting Time, in part, says, "You make all pertinent decisions about a spell (range, target, area, effect, version, and so forth) when the spell comes into effect" (Player's Handbook 174 and emphasis mine). Thus a creature need only possess the type animal exactly when the spell comes into to effect after its casting time of 24 hours is completed. An assistant can be on hand to make a Handle Animal skill check (DC 30) to push a magical beast that possesses an Intelligence score of 1 or 2 to drink the potion of aspect of the wolf at the appropriate time. (Or the assistant can simply render unconscious the magical beast then at his leisure take a full-round action to administer to the magical beast the potion; see Rules Compendium 84.)
This method is complicated, but the core rules provide an easier way. The 4th-level Sor/Wiz spell polymorph [trans] (PH 263) changes the subject's type, so, for example, a friendly wizard could transform a hippogriff into an ape right before his druid ally completes the casting of an awaken spell. As the awaken spell's duration is instantaneous, the subject'll retain the awaken spell's effects forevermore even after the polymorph spell's duration expires. (For more about constant targeting in 3.5 see here and here, although this should be less of an issue with a spell that has a duration of instantaneous.)
Note: The following addresses the concerns raised by this fine answer.
Multiple awaken effects can be abusive
Under the right circumstances, a creature can exploit its capacity to be the recipient of multiple awaken effects. This is usually a bad idea in moderation. The extra Hit Dice that come from being the subject of an awaken spell add to a creature's Effective Character Level (ECL), and it's a creature's ECL that determines when a creature gains class levels. It only takes a few extra animal HD from awaken spells—the effects of which are cumulative due to the spell's instantaneous duration—to make it so a creature effectively just won't gain class levels anymore, the gulf between its current XP total and the amount needed to reach its next effective level being simply too vast.
Still, all it takes to exploit multiple awaken spells is a wight (MM 255) and an accommodating reading of the rules. The path of least resistance is to have a creature voluntarily give up the saving throws against the 5th-level Drd and Sor/Wiz spell baleful polymorph [trans] (PH 202–3) so as to both gain the animal type and lose its humanlike sentience. This makes the creature a valid target for a friendly awaken spell. After that's cast, a dispel magic effect rids the creature of the baleful polymorph effect. Finally, the creature subjects itself to an ally's controlled wight's energy drain so as to remove from it the newly gained HD from the awaken spell. The creature ends this process with +1d3 Charisma and a rolled Intelligence score of 3d6 and no other harm done (except for, perhaps, the ensuing nightmares from the trauma).
A typical level 9 NPC caster charges 450 gp for a baleful polymorph spell and a level 9 NPC druid charges a 1,700 gp for an awaken spell, and making a wight requires only a +1 unholy arrow that has a price of 367 gp 1 cp. So under laboratory conditions a creature can realize a Charisma increase of +1d3 for under 2,500 gp, and, yes, that's abusive.
(A DM may disagree that the awaken spell's HD can be lost this way—see here. By the way, it's shockingly easy to create a wight or wight-like creature—see here and here, respectively.)
Further, for the right creature, it can be even more abusive to keep the extra HD from the awaken spell despite those HD counting toward the creature's ECL. Those extra awaken spell HD (and, of the increased Charisma, too) can be a shortcut to increasing the power of special abilities predicated on HD (common enough among some monsters), and, in addition to other effects of simply gaining HD, these extra HD count toward a creature's acquisition of ability score increases and feats, including epic feats.
Thus a barbarian or other noncaster might undergo the above process and opt not to expose herself to a wight simply to gain power asymmetrically. In fact, she might even be encouraged to do so by her caster allies! (The stronger she is, the better she is for the group, and the more money they can acquire to make her and themselves stronger.) Obviously, this, too, is abusive. The game barely accommodates 4 level 9 PCs; accommodating 2 level 9 casters and their level 9 warrior and maybe also their level 9 rogue both of whom have 10 or 30 or 100 extra animal Hit Dice means that the DM's rewriting the game.
What a DM can do about this
A gentlemen's agreement that applies equally to both sides of the screen that this simply won't be done is, of course, the best way to handle this. However, that sort of thing doesn't work for all groups. Still, were the players in my campaign considering this process, I'd offer such a gentlemen's agreement, making sure that I emphasized that the antagonists' resources far outstrip theirs.
If a mechanical solution were demanded, I'd likely implement the following house rule: The duration of the spell awaken and similar spells is permanent instead of instantaneous. This quashes layering multiple awaken spells but makes the awaken spell, for example, subject to dispel magic effects and areas of antimagic. While I'm certain such a house rule could send waves of devastation through some campaign settings, I suspect that in many campaign settings it'd barely make a ripple.
I've implemented a house rule like the above for the similarly instantaneous yet even more campaign-changing 5th-level Sor/Wiz spell fabricate [trans] (PH 229) and received little pushback from the players. I can't imagine my group pushing back harder against a similar house rule for the awaken spells. Of course, as always, your group may differ.
