"Illegal leaks from a corrupt & highly political Manhattan district attorney's office ... indicate that, with no crime being able to be proven ... the far & away leading Republican candidate & former president of the United States of America, will be arrested on Tuesday of next week," Trump wrote on Truth Social on Saturday.
A Trump spokesman said the former president had not been notified of any arrest.
Trump provided no evidence of leaks and did not discuss the possible charges in his post.
"Protest, take our nation back!" said Trump, whose supporters stormed the US Capitol building on January 6, 2021, to try to overturn his 2020 presidential election defeat.
The probe comes as Trump seeks the Republican nomination for the presidency in 2024.
No US president - while in office or afterward - has faced criminal charges.
Trump has said he will continue campaigning even if he is charged with a crime.
A representative for Manhattan District Attorney Alvin Bragg, whose office has been investigating a $US130,000 ($A194,000) hush payment Trump's former personal lawyer Michael Cohen made to porn actor Stormy Daniels, declined to comment.
Sources have said Bragg's office has been presenting evidence to a grand jury about the payment, which came in the waning days of Trump's 2016 campaign in exchange for Daniels' silence about an affair she said she had with Trump a decade earlier.
Trump has denied the affair happened and called the investigation by Bragg, a Democrat, a witch hunt.
Trump's claim about a Tuesday arrest was based on news reports that Bragg's office was going to meet law enforcement to prepare for a possible indictment, a person familiar with the matter said.
The Republican speaker of the US House of Representatives, Kevin McCarthy, on Saturday decried the investigation.
"Here we go again - an outrageous abuse of power by a radical DA who lets violent criminals walk as he pursues political vengeance against President Trump," McCarthy said on Twitter.
McCarthy's predecessor as speaker, Democratic Representative Nancy Pelosi, who like McCarthy was present at the Capitol when hundreds of Trump supporters stormed the building, denounced Trump's call.
Pelosi called Trump's announcement "reckless", adding: "He cannot hide from his violations of the law, disrespect for our elections and incitements to violence."
Trump's former vice president Mike Pence told ABC News Trump's possible indictment "just feels like a politically charged prosecution".
Asked about Trump's call for people to protest if he was indicted, Pence said he thought protesters would understand "they need to do so peacefully and in a lawful manner".
Bragg's office this month invited Trump to testify before the grand jury probing the payment, which legal experts said was a sign that an indictment was close.
Trump declined the offer.
In an email to staff on Saturday, reported by Politico and confirmed by Reuters, Bragg said "we do not tolerate attempts to intimidate our office or threaten the rule of law in New York ... We will continue to apply the law evenly and fairly and speak publicly only when appropriate".
Bragg's email did not mention Trump by name but cited "ongoing press attention and public comments surrounding an ongoing investigation".
Cohen pleaded guilty in 2018 to federal campaign finance violations tied to his arranging payments to Daniels and another woman in exchange for their silence about affairs they said they'd had with Trump, among other crimes.
He has said Trump directed him to make the payments.
The US Attorney's office in Manhattan did not charge Trump with a crime.
Trump is also confronting a criminal probe in Georgia over efforts to overturn the 2020 results in that state.
A special counsel is also investigating his handling of classified government documents after leaving office and his efforts to overturn the results of the 2020 election, which he lost to President Joe Biden.
Bragg's office last year won the conviction of the Trump Organization on tax fraud charges but Bragg declined to charge Trump himself with financial crimes.
