A draw by threefold is claimed, not offered.
If a three fold repetition (exact same board position reoccurring three times in a game) has already occurred, he can claim it and the game ends in a draw- you have no say. If this has happend in your game it sound like your opponent doesn't know how to claim a draw so I'd say be nice and accept the draw.
If your opponent can force a threefold repetition, or if he just thinks he can, he may offer the draw ahead of time to save you both from having to play it out. If you're not sure and you don't want to accept the draw, you don't have to.