The actor will not feature in upcoming spinoff The Bourne Legacy, which will be directed by Tony Gilroy and feature Jeremy Renner in the lead role.
Asked if he may return to the series, Damon told ShortList: "I'm keeping hope, man."
He added: "I was always fine with them doing another Bourne movie as long as it didn't preclude me and Paul from doing another Bourne.
"From what I understand, it doesn't at all, so that's fine. I really want to do another one with Paul and I'm sure it'll happen someday but for now they're doing this."
Damon was initially to star in the fourth Bourne movie but his character has seemingly been written out of the film.
When director Greengrass confirmed his exit from the franchise, Damon said that it would be a "bad idea" for him to make another Bourne film without him.
Damon said of his replacement in the series: "I'm a huge Jeremy Renner fan. I'm sure he'll be great."
Stacy Keach, Joan Allen, Albert Finney and Oscar Isaac are among the other actors reportedly in line to star in The Bourne Legacy.
Watch The Bourne Trilogy Blu-ray DVD trailer below: