Certain classes, theoretically, and in terms of story, should only be obtained by certain means besides leveling up. For example, sorcerers are theoretically born with their powers, and warlocks should have to gain them from divine beings. Paladins, too, in Keith Baker's (creator of the Eberron campaign setting) personal campaign, which he mentioned in his blog, have to be called in order to become a paladin. I was wondering if there are any official rules for these situations, or if it should just be left to the DM's discretion.
The prerequisite paragraph on page 163 of the PHB simply says
To qualify for a new class, you must meet the ability score prerequisites for both your current class and your new one, as shown in the Multiclasssing Prerequisites table.
That's it. That's the only requirement.
Now, on the other hand, from the same page...
This chapter defines two optional sets of rules for customizing your characters: multiclassing and feats. [...] Your DM decides whether these options are available in your campaign
So, according to the Player's Handbook, Multiclassing is an optional rule that the DM can allow. So a DM can forbid multiclassing altogether.
So, no. There are no additional requirements to multiclass besides "DM Says multiclassing is allowed in this game" and "I meet the ability score requirements."
Any further conditions applied are done so at the DM's discretion as Master of Rules.
There are no official rules for multiclassing prerequisites beyond what is listed under Chapter 6 of the PBH. Multiclassing is specifically covered on pages 163-166 and is an Optional rule to begin with (you can opt not to offer it, just like the Feats described later in that chapter.)
Anything additional would be a DM decision and homerule.