The rules don't say that it can't, so it should work
The opening in the rules: "spells such as raise dead."
The spell also effectively extends the time limit on raising the
target from the dead, since days spent under the influence of this
spell don’t count against the time limit of spells such as raise
dead. (PHB p. 245)
Which spells are in the category "such as" are not specified, nor are any specifically excluded. It is fair to rule that revivify is a spell "such as raise dead" in that it raises a creature from being dead, 0 HP, to being not dead, albeit with (only) 1 HP ... if cast in time. Timing is of the essence for gentle repose as well in this case, as gentle repose's description requires it to be cast within "such a spell's" time limit. One minute is revivify 's time limit.
Gentle Repose 2nd-level
Casting Time: 1 action
Cast gentle repose within a minute if all you have access to/funds for is a revivify spell. Cast revivify within the 10 days provided by gentle repose. The trick is to recognize that an ally is dead (not just incapacitated) in time to make the decision to cast gentle repose. In some situations, knowing that the character is dead will have taken you past the time limit/immediacy requirement and you not able to do this. The DM's ruling on that time will govern this.
Does this make sense? Yes.
What does this spell do? It give you time to get more powerful magic cast upon the body in order to get it out of "mostly dead" status and into "living" status. It isn't specified how potent that other (such as) spell is, just that it does enough to get up to 1HP, which means alive-not-dead. The threshold between "up and walking around" and "unconscious/incapacitated" (and thus mostly dead in this case) is that difference between 1 HP and 0 HP in D&D 5e.
The benefit from revivify(PHB p. 272).
That creature returns to life with 1 hit point. This spell can’t return to life a creature that has died of old age, nor can it restore any missing body parts.
The revivified creature can get up and walk around. The "gently reposed" creature has to be carried.
FWIW, the principle rules designer agreed with my assessment in Oct of 2016. (See user @36153's answer from 2017)