Sure! Tell him! What have you got to lose? If he likes you, then you'll know. If he likes someone else, then you can move on, but I'm betting he's just trying to get you to tell him you like him as it sounds like he likes you! Good luck!
So the guy I like just gave me a deal. He said, "If you tell me who you like, then I'll tell you who I like." I don't know if I should tell him. Should I tell him?
If you truly do like someone, there's no point not telling them. After all, the worst thing that can happen is that he doesn't actually like you in the same way. In that case, you've lost nothing. You were never together in the first place.
From what you're saying it looks like he already likes you, too. It's not definite, but there's certainly a reason why he wants to know who you like. It's possible that he's trying to make this deal because he's feeling a little shy.
Unless he's your best friend in the world and you tell him everything about your life, it's likely that he wants you to tell him that you like him first. This is probably because he's a little worried that you don't, and doesn't want to tell you before knowing that you share the same feelings.
Games
Of course, you could always ask him to reveal who he likes first. This may backfire though, as most people don't like to play games when it comes to things like romance.
If you really do like him, then I say go for it. You'll probably regret it if you don't.
Good luck, and fingers crossed that he likes you, too!