There was a scene on the Israeli version of The Office where the equivalent of Dwayne talked about how the religious woman working there has been pregnant for an unusually long time… so she is probably secretly an elephant.
Not quite sure what could be argued in case of a man―oh.
I think it's better to put "perhaps" at the beginning of the sentence - that's the more common thing, at least. But one can't really say "He is perhaps an elephant", because one can't really call something a "he" or a "she" unless they know what they're looking at. Instead of that, it's better to say "Perhaps it is/this is/that is an elephant". If it's indeed an elephant, then you can use the pronouns "he/she", depending on the animal's gender.