The notice came from the office of special counsel Jack Smith, The New York Times, CNN and other news outlets said, and gives the clearest sign yet that prosecutors are moving closer to charging the former president, who is seeking a return to the White House in 2024.
The Times, citing "two people familiar with the matter", said it was not clear when Trump's team had been told he was the subject of the investigation.
Special counsel Smith, named by Attorney General Merrick Garland, has been looking into a cache of classified documents that Trump had stored at his Mar-a-Lago residence after leaving the White House.
The FBI carted away some 11,000 papers after serving a search warrant on Mar-a-Lago in August, and Trump could face obstruction-of-justice charges after spending months resisting efforts to recover the trove.
Trump has repeatedly denied any wrongdoing.
"No one has told me I'm being indicted, and I shouldn't be because I've done NOTHING wrong," Trump posted on his Truth Social network Wednesday.
Investigators have been scrutinizing several suspected attempts to obstruct them from getting access to documents and footage from a security camera near the storeroom at Mar-a-Lago where documents were kept.
Trump has openly acknowledged taking and storing the documents, undermining his lawyers' suggestion that he took the stash inadvertently in the confusion of a chaotic departure.
Meanwhile, investigators have obtained an audio recording of Trump in which he acknowledged he held onto a classified Pentagon document after he left the White House, according to U.S. media.
On Monday, the media also reported that Trump's lawyers met with Justice Department attorneys.
John Rowley, James Trusty, and Lindsey Halligan were seen by reporters arriving at the Department of Justice building in Washington but did not make any comment.
The Washington Post reported at the time that Trump's lawyers had come to make their case that their client should not face any charges.
One expert told MSNBC that Wednesday's news would suggest an indictment is in the offing.
"If a prosecutor tells you that you are the target of their investigation, it means they expect to indict you," former federal prosecutor Renato Mariotti said.
"When I was on the other side of the aisle, when I was a federal prosecutor, when I told someone they were a target, that's what I meant."
Trump has already been charged with dozens of financial crimes as part of an alleged hush-money scheme to silence a porn star claiming she had sex with him, and is due to go on trial next March, in the middle of primary election season.
In addition to the hush-money and documents probes, Trump is being investigated over his efforts to overturn his 2020 election loss in the southern state of Georgia and his involvement in the January 2021 storming of the US Capitol by his supporters.
Other politicians have been found to have kept government documents at their private homes in recent months.
In January, Garland named a separate special counsel to examine whether President Joe Biden violated any law after the discovery of some classified documents at his former office and in the garage of his home in Wilmington, Delaware.