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The 38-year-old actor had previously said that the screenplay for the latest Bourne instalment was not finished. Universal Pictures recently hired Josh Zetumer to write an alternate script for the long-awaited project.
Damon has now revealed that there is a great deal of "pressure" to make the sequel.
He told Empire: "Because even if we made a horrible movie, it would make money, and they know that. There's a huge amount of pressure.
"But it's not like somebody's hammering at our door. It's just that they would love to make another Bourne movie, and I understand why. It's so hard to have a sure thing in Hollywood, and this is as close as you get. So, from an executive's standpoint, I get it."
He added: "Maybe, if we can figure out a good story. If you have a good fourth Bourne story, call Universal and they'll give you a bunch of money!"
It was recently reported that Damon will be honoured with the American Cinematheque Award.
His next film The Informant! is released in cinemas on September 18 in the US and on November 20 in the UK.
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