US President Donald Trump has threatened to sue The Wall Street Journal after it published a story about an alleged off-colour letter written by him to late disgraced financier Jeffrey Epstein that featured a drawing of a naked woman.

The Journal story, which quickly reverberated around the US capital, says the note to Epstein bearing Trump's signature was part of a collection of notes for Epstein's 50th birthday in 2003. The newspaper says it reviewed the letter but did not print an image.

"The Editor of The Wall Street Journal... was told directly by [White House press secretary] Karoline Leavitt, and by President Trump, that the letter was a FAKE," Trump wrote in a post on his Truth Social network.

"Instead, they are going with a false, malicious, and defamatory story anyway," he said.

"President Trump will be suing The Wall Street Journal, NewsCorp, and Mr. [Rupert] Murdoch, shortly. The Press has to learn to be truthful, and not rely on sources that probably don't even exist."

The alleged letter – which Trump denies writing – is raunchy, as were others in the collection, the Journal reported. It contains several lines of typewritten text, contained in an outline of a naked woman drawn with a marker.

"The future president's signature is a squiggly 'Donald' below her waist, mimicking pubic hair," the Journal reported. "The letter concludes: 'Happy Birthday – and may every day be another wonderful secret.'"

Trump denied writing the letter or drawing the figure, telling the Journal: "This is not me. This is a fake thing."

"I don't draw pictures of women," he said. "It's not my language. It's not my words."

Murdoch, who controls the NewsCorp media empire, was in Trump's suite on Sunday at MetLife Stadium outside New York City for the Fifa Club World Cup final.

The Republican president was already facing a firestorm over his past relationship with Epstein, and claims that his administration is covering up lurid details of Epstein's crimes to protect rich and powerful figures.

Epstein died by suicide in a New York prison in 2019 – during Trump's first term – after being charged with sex trafficking in a scheme where he allegedly groomed young and underage women for sexual abuse by the rich and powerful.

The Trump-supporting far-right has long latched on to the scandal, claiming the existence of a still-secret list of Epstein's powerful clients and that the late financier was in fact murdered in his cell as part of a cover-up.

Trump supporters expected the Republican to answer their questions on his return to office this January but now find themselves being told the conspiracy theories are false. (AFP)