It's not impossible, but I think it is risky.
I already believe that trying to be friends with an ex is almost always a bad idea. The history you have with someone never changes. In your situation, two things concern me: one, that your ex is the one pushing for the friendship, and two, that he "brings up the past a lot in a sentimental, almost longing way." I get the feeling that he wants to be more than friends. I could be wrong, but if I'm not, what will you do when he starts pushing for more?
You must consider how being friends with your ex might affect your current relationship. Will your new guy be okay with it? Even if he says he is, you are still bringing a potentially stressful element into your relationship. It's one thing agree to something in theory, but if and when your ex starts coming between you and your new guy, I can assure you that New Guy won't be okay with it.
Your ex might be a stand-up chap. You might love having him in your life again. You just have to decide if doing so is worth risking complications in your new relationship. Me, I'm from the "if it ain't broke, don't fix it" school of thought.
Good luck. Thanks for the question.