The former president was told that he could appear before a Manhattan grand jury next week if he wishes to testify, a strong indication that an indictment could soon follow.

The Manhattan district attorney’s office recently signaled to Donald J. Trump’s lawyers that he could face criminal charges for his role in the payment of hush money to a porn star, the strongest indication yet that prosecutors are nearing an indictment of the former president, according to four people with knowledge of the matter.

The prosecutors offered Mr. Trump the chance to testify next week before the grand jury that has been hearing evidence in the potential case, the people said. Such offers almost always indicate an indictment is close; it would be unusual for the district attorney, Alvin L. Bragg, to notify a potential defendant without ultimately seeking charges against him.

In New York, potential defendants have the right to answer questions in the grand jury before they are indicted, but they rarely testify, and Mr. Trump is likely to decline the offer. His lawyers could also meet privately with the prosecutors in hopes of fending off criminal charges.

Any case would mark the first indictment of a former American president, and could upend the 2024 presidential race. It would also elevate Mr. Bragg to the national stage, though not without risk, and a conviction in the complex case is far from assured.

Mr. Trump has faced an array of criminal investigations and special counsel inquiries over the years but has never been charged with a crime, underscoring the gravity of Mr. Bragg’s inquiry.

Mr. Bragg could become the first prosecutor to charge Mr. Trump, but he might not be the last.

In Georgia, the Fulton County District Attorney is investigating whether Mr. Trump interfered in the 2020 election, and at the federal level, a special counsel is scrutinizing Mr. Trump’s effort to overturn the election results, as well as his handling of classified documents.

The Manhattan inquiry, which has spanned nearly five years, centers on a $130,000 payment to the porn star, Stormy Daniels, in the final days of the 2016 presidential campaign. The payment was made by Michael Cohen, Mr. Trump’s former fixer, who was later reimbursed by Mr. Trump from the White House. Mr. Cohen is expected to testify in front of the grand jury, but has not yet done so.