The purpose for the constitutional law that American presidents must be born in America is because of loyalty to America and only America. We could never be sure someone born in another country would always have America's best interests in mind.
"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." – Section 1 of Article Two of the United States Constitution, under clause 5.
Being the President of the United States of America, as un-American as it seems, should remain the preserve of the American born and raised people...
No other country... let me repeat that... NO OTHER COUNTRY allows foreign nationals to lead their country.
As a person who has never been on the US nor has any sort of link with it as a country, i'd still answer No. A country is just a country. If someone that's not been born and raised on it wishes to govern it, it most likely isn't because he likes the beaches and shores.
Even if the US is currently the biggest and most globalized country in the world, historically, this is just a fad. And you'd be doing yourself no favors giving control of such a heavily nationalist culture to a foreigner.