Well your opponent wouldnt have to ask you, but could ask if he wanted. He could also simply consider the offer, but it may be that there is only one hard to find good move and your opponent is offering you a draw because he isnt sure he's found it, in which case you might want to have him make a move.
Fide says this
"A player wishing to offer a draw shall do so after having made a move on the chessboard and before stopping his clock and starting the opponent`s clock. An offer at any other time during play is still valid, but Article 12.6 must be considered. No conditions can be attached to the offer. In both cases the offer cannot be withdrawn and remains valid until the opponent accepts it, rejects it orally, rejects it by touching a piece with the intention of moving or capturing it, or the game is concluded in some other way."
Where 12.6 simply forbids annoying the opponent in any way, including unreasonable draw offers.
So I believe if your opponent requests you make a move first, that is a rejection but with a 'feel free to offer again after you have moved and I wont consider it unreasonable'.
If I am offered a draw but I want to see my opponents move before deciding that is not a rejection of the draw offer. I am entitled, by the rules, to see his next move before deciding and he cannot retract his offer, it is binding. It is only a rejection if I verbally decline his offer or if I make my next move after his offer.
Unsportsman-like Behavior...
I do not know if the Clock stops if your Opponent Offers a Draw on His Turn.
ADK