According to the Cambridge Dictionaries:
Maybe and perhaps are adverbs that mean the same thing. We use them when we think something is possible, but we are not certain. We use maybe mostly in front or end position whereas perhaps is used in front, mid and end position.
A: Have you seen my glasses? I can’t find them anywhere.
B: Maybe you left them at work.
A: Do you think these shoes are too high?
B: They are perhaps. (it’s possible but I’m not certain)
As you perhaps remember, I worked as an interpreter for three years in the European Parliament.
Not: As you maybe remember...
Perhaps is slightly more formal than maybe:
He was, perhaps, a little too smartly dressed for a holidaymaker.
Maybe I’ll finish work early tomorrow and go shopping with you.
