The 56-year-old star is taking a break from acting to direct Damon in his new movie, Suburbicon.
Clooney appeared on Jimmy Kimmel Live earlier this week to promote the movie, when the host started asking some Damon-baiting questions.
Kimmel asked: “Was this a challenge you gave yourself? ‘Can I make a great movie with a terrible actor?’
Clooney replied deadpan: “Oh you’re talking about Matt you mean?”
Clooney continued: “Well we got Matt because we couldn’t afford Brad Pitt. Y’know Brad’s expensive.
“And Matt’s kinda…he’s on that side on the way down now, so we got him at a pretty good discount. Much cheaper that way.”
Damon, who has had a jokey feud with Kimmel for the best part of the decade, appeared on the show later on with what was supposed to be the Clooney twins.
The actor ended up getting “angry” with the pair for ganging up on him and gave them the finger before security took him away.
Last year Ben Affleck claimed Damon was bitter he was Batman.
Affleck poked fun at his life long friend, teasing him for overplaying Bourne.
He said: “He’s very bitter. All he gets to do is Jason Bourne. Just keeps doing it again and again. We get it.”