Gov. Arnold Schwarzenegger (search) says he would be interested in running for president if the Constitution were amended to allow naturalized citizens to seek the nation's highest office.

During an interview for Sunday's CBS program "60 Minutes," Schwarzenegger said, "Yes, absolutely" when asked if he would like to run and would support such an amendment.

Schwarzenegger, 57, had previously deflected the question.

"I think, you know, because why not? I mean, you know, anyone with my way of thinking, you always shoot for the top," the governor said. "But it's not something that I am preoccupied with.

"I am not thinking one single minute about that because there's so many things I have to do in California, and my promise was to straighten out the mess in California," he said.

Schwarzenegger, a native of Austria (search), came to the United States in 1968 and built a fortune as a champion body builder and actor. He won his first bid for public office in last year's gubernatorial recall election in California.

Article II of the Constitution prohibits naturalized citizens from being president.

"No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of president," the historical document states.

Sen. Orrin Hatch (search), R-Utah, chairman of the Senate Judiciary Committee, has proposed an amendment that would allow immigrants to run for president after being citizens for 20 years. Schwarzenegger became a citizen in 1983.