No Damon as Kirk

He would make a good Kirk, though.

he was asked about the rumors that he's up for the role of Captain James T. Kirk in J.J. Abrams' forthcoming Star Trek reboot.

Damon's reaction was a pleasantly succinct 'no' but wasn't averse to the idea. Damon says has heard the internet rumor and Shatner's welcome response to the idea, he even asked J.J. Abrams about the talk.

Abrams responded that they're looking for someone young to play the younger Kirk, an actor in his twenties. It's expected that the official Trek announcements are to be made at Comic-Con and Zachary Quinto (Sylar on "Heroes") is still the favirite to play the young Spock.