I recently heard a rumor that George Washington was offered to become king of America, but refused instead wanting a Presidency; is this rumor true or is it just just that, a rumor?
An elaboration on my comment; the bad idea came from my distant cousin, John Adams!
No, this is completely a myth.
There were many presidents prior to Washington, just not one that encompassed the entire United States. Some states had presidents that represented them during the revolutionary period (1774-1778) but prior to the formation of the U.S. federal government.
The idea of a rejection sounds good to modern readers, but the idea of a king was never entertained by the U.S. forefathers. They had, much to their credit and patriotism, more sense than that. The myth comes probably from correspondence with Lewis Nicola, at a much later date. Some letters he wrote to Washington eludes to the idea, but does not state it or spell it out.