According to a recent interview with J.J. Abrams, he approached Matt Damon first with the offer to give him the George Kirk role, but he declined. Originally it was believed that Damon was up for James T. Kirk, but according to Abrams that was never the case.
http://movies.ign.com/articles/104/1049407p1.html
http://movies.ign.com/articles/104/1049407p1.html