The actor played Jason Bourne in the first three instalments of the spy series, but pulled out of a fourth movie along with director Paul Greengrass and was replaced by Jeremy Renner.
Damon has now admitted that he wants the Tony Gilroy-directed film to succeed so that he and Greengrass may still have a chance to "reboot" the franchise.
"If you look at the first three movies, we kind of pounded that idea of identity and amnesia into the ground," he told GQ. "We really got everything out of it that we could. So to reboot it, we need to come up with something completely new.
"[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."
Damon also shed light on the troubled production of 2007's The Bourne Ultimatum, which he blamed on a "terrible" rough script submitted by Gilroy under a big-money deal.
"It's really the studio's fault for putting themselves in that position," he said. "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.
"We had a start date. Like, 'It's coming out August of next year'. We're like, 'Hang on, we've got to figure out what the script is'."
Renner has said that he would like team up with Damon for a future Bourne movie.
The Bourne Legacy, which also stars Edward Norton, Rachel Weisz and Joan Allen, is set for release on August 3, 2012 in the US and August 17, 2012 in the UK.
Watch Matt Damon in the trailer for his new film We Bought a Zoo below: