The 49-year-old played Fox Mulder in the TV series from 1993 until 2002. He also reprised his role in two X-Files feature-length films; 1998's Fight The Future and 2008 sequel I Want To Believe.
The Californication star told The Daily Beast that he would like to see the plotline for the possible third instalment centre on an "alien-oriented conspiracy".
He said: "As far as the X-Files movie I'd like to do next, if we get a chance to do it, would be a return to the heart and soul of the mythology, which is the alien-oriented conspiracy."
He added: "I think it's natural for The X-Files to have another movie in 2012, so we'll see if we get to do it."
Co-star Gillian Anderson previously hinted that a third film is in the works and that she is on board to play Dana Scully.