The Welsh actor, who has played former Prime Minister Tony Blair in The Deal and The Queen, joked that he would be more interested in a role as Obama than reprising Blair for a third time.
Sheen referenced Robert Downey Jr. as a recent example of a white actor playing a black character on film.
"I want to play Obama!" he said. "Why would I want to play Blair? If Robert Downey Jr. can do it in Tropic Thunder then I'm ready to play Obama!"
Sheen signalled out the new President for praise, saying that his election had "re-engaged" Americans in politics.
"I think people had kind of given up on it (politics) during the Bush years and with the Iraq war," he said. "I think they now begin to feel like they have more of a say in things and may be more represented, or certainly people who didn't feel represented before maybe feel that they are now."
Sheen's new movie Frost/Nixon, which centres on TV presenter David Frost's interviews with a post-Watergate Richard Nixon, is released on Friday.