Reporting by CBS News' Paula Reid and Kathryn Watson

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

This comes after the New York Times published a story last week claiming Rosenstein brought up the 25th Amendment and taping the president. Rosenstein remains the deputy attorney general despite reports that he had resigned. A source familiar with the situation told CBS News' Paula Reid Rosenstein has expected to be fired. Sanders says that Rosenstein is scheduled to meet with the president Thursday, once he returns to Washington from the U.N. General Assembly.

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On Monday, Rosenstein was at the White House, meeting with White House chief of staff John Kelly and then attending a previously scheduled Cabinet meeting.

Should Rosenstein resign or be fired, oversight of special counsel Robert Mueller's Russia probe would be passed to Solicitor General Noel Francisco, according to the Justice Department. It's possible Mr. Trump would use the Vacancies Reform Act to appoint a new acting deputy attorney general.

Mr. Trump left open the possibility of relieving Rosenstein of his duties in an interview with Geraldo Rivera.

"I don't want to comment on it. I don't want to comment on it until I get all the facts. I haven't gotten all the facts," the president said in the radio interview that aired Monday. "But certainly it's being looked at in terms of what took place, if anything took place, and I'll make a determination sometime later."

The president has also expressed frustration with Attorney General Jeff Sessions. Mr. Trump blames Sessions for recusing himself in the Russia investigation, which is why Rosenstein is in charge of the probe. Mr. Trump has lamented that, "I don't have an attorney general," and has largely declined to comment as to whether he will oust Sessions eventually.