Will fans ever see the story of Jason Bourne continue with original star Matt Damon?

Damon portrayed trained killer Jason Bourne in three installments of the Paul Greengrass directed franchise: "The Bourne Identity" (2002), "The Bourne Supremacy" (2004) and "The Bourne Ultimatum" (2007). In 2012, Tony Gilroy, screenplay writer for all three previous films, directed a fourth film, "The Bourne Legacy," which starred Jeremy Renner as agent Aaron Cross.

Damon recently revealed that he could be re-Bourne into the franchise, but he said he would only sign onto another Bourne film if the project was directed by Greengrass.

"I've always been open to it if, you know, Paul Greengrass is the director," Damon told CNBC.

"It felt like such a good way to end it the last time," Damon continued. "Having said that, I loved that character, and I'd love to see what happened to him."

The only problem is Damon and Greengrass can't think of what's next for their agile hero.

"We've just never been able to come up with a story," Damon said.

Another Bourne movie is in the works, but considering Damon's firm stance on the issue, we'll have to wait a while to see him return to the role. The new Bourne film will star Renner again, while Justin Lin ("Fast & Furious 6") will direct.

Damon isn't giving up, however. The actor thought of the perfect group of people to hit up for some creativity.

"If any of you viewers have a story please call Universal [Studios] and submit it," Damon added.

While he waits for those pitches, the actor is congratulating his friend, George Clooney, on his recent engagement to Amal Alamuddin.

"I'm just thrilled that he met Amal and that they're ... as happy as they are," he told Closer magazine this week. "He deserves it."

Despite Hollywood's reaction, Damon said that he wasn't surprised to hear the news. When it comes to the possibility of Clooney being a father, however, Damon doesn't quite have the answers.

"You got to ask him that one," he said smiling. "I don't know."

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Follow Scharon Harding on Twitter: @SH____4.