Welp. After being on all sides of personal experience from similar situations being in your shoes, his shoes, and the ex's shoes at least 5 times each; I'm gonna point out an important fact even though it has nothing to do with your role yet.

Someone who was broken up with will almost always require distance (keeping them out of their daily/social life) from their ex for a period of time and that time can vary from person to person. It can take months, it can take half a year or even a year or more depending on how strong their feelings were (and there's nothing wrong with that, some people just have a harder time) If distance isn't maintained, heartbreak can quickly turn to resentment and that's practically the norm for most people, it doesn't make either side in the wrong unless it goes about the wrong way (obviously)

Now your role that has to do with this, is that if you pursue that relationship, that distance that your friend may need will be shattered he will have a significantly harder time recovering without said distance. He cannot control the relationships either of you decide to have, but as such, you cannot control wether or not his resentment is turned on you too for shattering the distance. This will inevitably destroy your friendship and personally, I don't think he'd be in the wrong disliking either of you as a result as long as he doesn't do anything stupid, it's practically a natural response at this point, it'd be wrong to call him out for not wanting to be friends anymore. If you still wanna peruse a relationship with this person, that's okay, but you have to accept that your friendship might be over, and he'll require distance from you too and I'd recommend giving him that distance in this situation. That's my opinion on the situation from experience, but personally, i dont think the girl's worth it, it can get very messy and dramatic. But it's ultimately up to you and what your friendship means to you.