without a Constitutional Amendment which isn't going to happen. The Constitution requires a person be born in the US to qualify for the presidency (and the vice presidency by extension). From Article II, Section 1:

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; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.

So, he obviously isn't running for California Governor with hopes of being the president one day.