"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.
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.
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.
The idea that people born in America would be more loyal to America than somebody that has actually changed his citizenship is patently absurd.
When this country was founded and the framers wrote the constitutional requirement that the president to be a "natural born citizen", scholars concede that the 1787 Constitutional Convention's deliberations shed little light on the reason for the natural born requirement. So they instead cited a letter sent to George Washington during the Convention by John Jay, who would later become the nation's first chief justice.
Jay was wary of entrusting foreigners with positions of power. Presumably concerned that foreigners might harbor allegiances to their native countries, he advocated for "a strong check" on admitting them into government and, in the first known use of the term, warned that the commander in chief position should be given only to a "natural born citizen."
Many of the founders and framers expressed fear of foreign influence on the person who would in the future serve as President of the United States since this particular office was singularly and uniquely powerful under the proposed new Constitution. This question of foreign influence was elevated when John Jay considered the additional power granted to the Presidency during times of war, that is when he serves as Commander in Chief of the military. Jay felt strongly that whoever served as President and Commander In Chief during times of war must owe their sole allegiance to and only to the United States.
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.