Damon played Jason Bourne in three installments of action spy series, but decided against signing on for last year's (13) The Bourne Legacy, which starred Jeremy Renner.
Now the Oscar winner reveals would consider a comeback to the series, but stipulates that Greengrass, who directed The Bourne Supremacy (2004) and The Bourne Ultimatum (2007), would have to be behind the camera.
Damon told U.S. news network Cnbc on Sunday (04May14), "I've always been open to it if Paul Greengrass is the director. We've just never been able to come up with a story."
He quipped, "So if any of your viewers have a story, please call Universal (Studios) and submit it."
And while Damon believes Bourne received a satisfying ending at the end of the third film, he's still curious to see what the secret agent has been up to in the past couple of years.
He said, "If felt like such a good way to end it the last time. But having said that, I love that character and I'd love to see what happened to him."
Renner will reprise his role as Aaron Cross for a fifth Bourne movie due out next summer (15).