Filmmaker Michael Moore recently praised Damon for standing up for his beliefs and called on the star to launch a presidential campaign.
Moore said at the time: "I think that [Damon] has been very courageous in not caring about who he offends by saying the things that need to be said here, and if you want to win, the Republicans have certainly shown the way - that when you run someone who is popular, you win."
A photographer recently questioned Damon on whether he has any plans to enter politics, prompting the actor to reply: "No sir!"
Damon added to TMZ: "I think there are probably better choices out there."
The Oscar winner supported US President Barack Obama in the 2008 elections, but recently admitted that he has been disappointed by Obama's first term of office.
Damon attended a teachers' rally last month to support changes to standardised school testing for students.
He will next star with Gwyneth Paltrow and Marion Cotillard in Contagion, which opens on September 9 in the US and on October 21 in the UK.
