President Donald Trump will meet with Deputy Attorney General Rod Rosenstein on Thursday amid swirling reports that the No. 2 Justice Department official's departure is imminent.

"At the request of Deputy Attorney General Rod Rosenstein, he and President Trump had an extended conversation to discuss the recent news stories," White House press secretary Sarah Huckabee Sanders said in a statement.

"Because the President is at the United Nations General Assembly and has a full schedule with leaders from around the world, they will meet on Thursday when the President returns to Washington, D.C."

Axios published a bombshell report Monday that Rosenstein is resigning, citing sources with knowledge.

But the report was contradicted by other news outlets, including from NBC News' Pete Williams, who reported that Rosenstein would not resign of his own accord after his off-the-cuff comments about possibly recording and removing Trump were revealed last week.

He will only depart if the White House fired him and will refuse to resign if asked to do so, Williams reported. News of Rosenstein's potential departure was a "huge shock" to the Justice Department, Williams added.

Although Trump has sharply criticized Rosenstein over the Russia probe, his departure could create a big problem for the White House: filling the position six weeks before the crucial midterm elections.

A Justice Department official told The New York Times that if Rosenstein is out, then Solicitor General Noel Francisco would oversee the Russia investigation.

Shortly after the resignation reports, Rosenstein was at the White House for a previously-scheduled principals meeting, a Justice Department official told NBC. Trump arrived in New York City on Sunday for the United Nations General Assembly. He was scheduled to have dinner with Japanese Prime Minister Shinzo Abe that evening.

Bloomberg reported that Rosenstein told White House chief of staff John Kelly that he would resign, citing a person familiar with the matter.

Rosenstein's possible departure will immediately raise questions about the fate of the ongoing investigation by Mueller, who is probing Russian interference in the 2016 presidential election, and possible obstruction of justice by Trump.

The special counsel's office declined to comment on the report.

Rosenstein's job security was called into question after the Times reported last week that the No. 2 DOJ official had discussed invoking the 25th Amendment to remove Trump and had talked about surreptitiously recording the president.

Other reports, however, suggested that Rosenstein was being sarcastic when he made those comments.

In an interview with radio host Geraldo Rivera over the weekend, Trump hinted that he was considering firing Rosenstein.

"Certainly it's being looked at in terms of what took place, if anything took place. I'll make a determination sometime later but I don't have the facts," Trump said when asked if he would cut Rosenstein loose over the reports.

Rosenstein oversees the special counsel investigation, and has appointed Mueller to run the Russia probe last year, after Attorney General Jeff Sessions recused himself from the case.

The White House did not immediately respond to CNBC's request for comment on Axios' report. The Justice Department did not immediately respond to CNBC's inquiry.

Trump has repeatedly blasted Mueller's inquiry, which also is focused on possible collusion with Russia by members of the Trump campaign.

He has called the investigation a "witch hunt," and has repeatedly vented frustration about Sessions' recusal, which directly led to Mueller's appointment by Rosenstein.