Speaking with GQ about his latest movie We Bought A Zoo, Damon mentions why he wouldn't return to any further Bourne movies:
"If you look at the first three movies, we kind of pounded that idea of identity and amnesia into the ground. We really got everything out of it that we could. So to reboot it, we need to come up with something completely new."
He also touched on Tony Gilroy's failed Bourne Ultimatium script which was heavily rewritten:
"I don't blame Tony for taking a boatload of money and handing in what he handed in. It's just that it was unreadable. This is a career-ender. I mean, I could put this thing up on eBay and it would be game over for that dude. It's terrible. It's really embarrassing. He was having a go, basically, and he took his money and left."
Damon admits that Jeremy Renner's casting was "A surprise." But that he hoped the movie did well "[I’m] really pulling for this one, even though I don’t have anything to do with it. Selfishly, it’s bad for me if that movie doesn’t do well."

It's refreshing to see that Damon wouldn't return to the role just for the sake of another movie. While it would have been interesting to see where Jason Bourne would go next, it's easy to see Damon's point. While there may be some tension about the script, it seems Damon wishes everyone well. Since Renner is not playing Bourne, there are some rumors about a future return of Bourne in some capacity.
What say you?