The chances of Deputy Attorney General Rod Rosenstein leaving his job or being fired appeared to be fading early Monday afternoon, after a source familiar with his status said he never offered his resignation, and only talked about it after a New York Times report from last week said Rosenstein was trying to orchestrate President Trump's removal from office.

Rosenstein returned to the Justice Department around 1 p.m. Monday after a previously scheduled noon meeting at the White House, still in his position as the department's No. 2.

According to the White House, Rosenstein and Trump spoke Monday in an "extended conversation" about the Times report, as the president is in New York for the United Nations General Assembly. The two will meet in person on Thursday in Washington, Press Secretary Sarah Huckabee Sanders said.

A report from Axios early Monday morning said Rosenstein offered his resignation, and others said he was expecting to be fired at the White House on Monday. But the source told the Washington Examiner that Rosenstein and White House chief of staff John Kelly spoke over the weekend and though resignation was discussed, Rosenstein never formally offered his.

According to the White House, Rosenstein and Trump spoke Monday in an "extended convesation" about the New York Times report, as the president is in New York for the United Nations General Assembly. The two will meet in person on Thursday in Washington, Press Secretary Sarah Huckabee Sanders said.

Last week, the New York Times reported that Rosenstein discussed invoking the 25th Amendment to remove Trump from office, and considered wearing a device to record the president. Rosenstein rejected that report, but many conservatives said the story was enough to prompt Trump to fire him.

That speculation led to several conflicting reports Monday that alternatively said Rosenstein was fired, that he was expecting to be fired, or that Rosenstein was expected to resign.

[Also read: Lisa Page believed Rod Rosenstein was serious about secretly recording Trump: Report]

Rosenstein, a Republican appointed by Trump, oversees special counsel Robert Mueller’s investigation, and his removal would raise immediate questions about who succeeds him and who oversees the Mueller probe. Solicitor General Noel Francisco is the next Senate-confirmed Justice Department official in line, meaning he would likely take over Mueller’s investigation immediately after Rosenstein's departure, assuming he is not appointed acting deputy attorney general.

If Rosenstein resigned and Francisco were appointed acting deputy attorney general, then the assistant attorney general in charge of the Office of Leagl Counsel, Steven Engel, would take over Mueller's investigation, according to a Justice Department memo.

Trump has railed against the Justice Department for the Russia investigation, though most of that ire is directed at Attorney General Jeff Sessions. Sessions’ recusal from the Russia investigation opened the door for Rosenstein to appoint Mueller.

Fired FBI Deputy Director Andrew McCabe, whose memos suggested Rosenstein considered secretly recording Trump, said he was concerned if Rosenstein were fired.

“To be clear, I had no role in providing information of any kind to the media stories about events following Director Comey's firing. If the rumors of Deputy AG's Rosenstein’s departure are true, I am deeply concerned that it puts that investigation at risk,” said McCabe in a statement.

This story was updated at 1:12 p.m.