U.S. CONSTITUTION - Article 2 - 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 is free to run as VP, but not as P. Got it. The Speaker of the House would move up to next in line.