The Austrian-born former movie actor, who won a landslide victory in a snap California election late last year, made the comments in a television interview.
Current law makes the office available only to native-born citizens, but Senator Orrin G. Hatch of Utah has introduced a resolution proposing an amendment that would allow a foreign-born person who has been a US citizen for at least 20 years to be a candidate.
When asked on the NBC News programme "Meet The Press" whether he supported such an amendment, Schwarzenegger replied, "Oh, absolutely".
"I think that there are so many people here in this country that are now from overseas, that are immigrants, that are doing such a terrific job with their work, bringing businesses here," he said.
"There is no reason why not".
"Look at the kind of contribution that people like Henry Kissinger have made, Madeleine Albright," he said, referring to two former secretaries of state who were born in Europe and were therefore prevented from running for the country's highest elected office.
Though Schwarzenegger is a political neophyte who has yet to prove himself in California, the comments were seen as significant because his career is often compared to that of Ronald Reagan, who was also an actor and California governor before becoming president.
Schwarzenegger however declined to say if he was planning a presidential bid. "I haven't thought about that at all," he said.
"I tell you that I'm so busy with our state. You know, California is a big state and a very complicated state. Right now I concentrate just on that". – Sapa-DPA.
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