NEW YORK (Reuters) - Donald Trump offered to pay $5 million to the charity of President Barack Obama's choice if Obama releases his college and passport records, the real estate mogul and television personality said on Wednesday.

"Frankly, it's a check that I very much want to write," Trump said in a YouTube video released via his Twitter and Facebook pages.

Trump has questioned whether Obama's birth certificate issued by the state of Hawaii is legitimate, suggesting Obama was not born in the United States, which could have made him ineligible for the White House. The White House released the long-form copy of Obama's birth certificate in 2011.

Trump did not say what he expected the college and passports records to reveal but was specific in saying he wanted to see all of Obama's college applications and records and his passport applications and records.

"President Obama is the least transparent president in the history of this country," Trump said in the video.

"If he releases these records it will end the question and indeed the anger of many Americans."

Trump, who had toyed with the idea of running for the 2012 Republican presidential nomination, said the deadline for the release of the documents was 5 p.m. (2100 GMT) on October 31.