A spokesperson for the district attorney's office declined to comment.
Trump said, without providing evidence, that "illegal leaks" from the Manhattan district attorney's office indicated that he would be arrested. He did not say what the charges would be.
"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.
"Protest, take our nation back!" Trump said.
Manhattan District Attorney Alvin Bragg's office earlier this year began presenting evidence to a grand jury investigating a $130,000 payment that Michael Cohen, Trump's former personal lawyer and fixer, made to porn star Stormy Daniels in the waning days of Trump's 2016 campaign.
Daniels, whose real name is Stephanie Clifford, says she had an affair with Trump a decade earlier. Trump has denied the affair happened.
Trump was Republican president from 2017 to 2021 and has said he will make a bid to return to the White House in the 2024 US presidential election.
Bragg's office earlier this month invited Trump to testify before the grand jury probing the hush money payments, according to Trump's lawyer, Susan Necheles. Legal experts said that was a sign that an indictment was close.
Cohen pleaded guilty in 2018 to federal campaign finance violations tied to his arranging payments to Daniels and another woman, 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.
Cohen testified before the grand jury on Monday and again on Wednesday, according to his lawyer, Lanny Davis. Grand jury proceedings are not public.
Daniels' lawyer said she spoke with prosecutors last week.
The probe is one of several legal woes Trump faces as he seeks the Republican nomination for the presidency.
Trump is also confronting a state-level criminal probe in Georgia over efforts to overturn the 2020 results in that state.
A special counsel named by US Attorney General Merrick Garland is currently investigating Trump's handling of classified government documents after leaving office, as well s his efforts to overturn the results of the 2020 election, which he lost to President Joe Biden, a Democrat.
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 related to his business practices, prompting two prosecutors who worked on the probe to resign.
Trump leads his early rivals for his party's nomination, holding the support of 43% of Republicans in a February Reuters/Ipsos poll, compared with 31% for his nearest rival, Florida Governor Ron DeSantis, who has not yet announced his candidacy.