Mr Trump, who led the charge in the so-called birther conspiracy, said he would make an announcement on Wednesday that could "possibly" change the race for the White House.
"[I have] something very, very big concerning the president of the United States," he told Fox and Friends this week. "It's going to be very big. I know one-thing – you will cover it in a very big fashion."
The billionaire did not give further details but said the announcement would be made via Twitter and Facebook.
However, Douglas Kass, an investor who appeared on the same business talk show as Mr Trump, said the real estate tycoon would claim to have unearthed divorce papers between Barack and Michelle Obama.
"High above the Alps my Gnome has heard that Donald Trump will announce that he has unearthed divorce papers between the Prez and his wife," the businessman told his 48,000 followers on Twitter.

The White House has previously been forced to deny rumours that the couple were on the verge of splitting up in 2000 following claims in the controversial Ed Klein book The Amateur.
The book, which was rubbished by critics as "fiction", also claimed the president had been depressed and suicidal after a failed election bid in Chicago.
At the time Eric Schultz, a spokesman for the president, said: “Ed Klein has a proven history of reckless fabrication in order to sell books. Nobody in their right mind would believe the nonsense in this one."
Trump has a dubious record when it comes to allegations about Barack Obama – most notably with the "birther conspiracy", which led some to question why Mitt Romney has failed to distance himself from the mogul.
Commenting in May on the potential embarrassment Trump could cause to the Romney campaign, George Will, the conservative commentator, said: "I do not understand the cost benefit here. The cost of appearing with this bloviating ignoramus is obvious, it seems to me."
The "birther conspiracy" was eventually laid to rest in 2011 after the White House released President Obama's birth certificate showing he had been born in Hawaii and not Kenya as Trump had relentlessly insisted.