Former New York mayor Rudy Giuliani, another Trump backer who was linked by press reports to the post of attorney general, told CNN on Monday he did not want the job and would have recused himself if he had been in Sessions' position.
"As the president said yesterday, he was disappointed in Attorney General Sessions' decision to recuse himself".
Trump has recently decried what he says is a double standard between the scrutiny over his associates' interaction with Russian officials and the investigation into Clinton's use of a private email server while secretary of state.
The Washington Post said replacing Sessions is viewed by some Trump associates as potentially part of a strategy to fire special counsel Robert Mueller and end his investigation into whether the Trump campaign coordinated with Russian Federation to influence the election.
Mr Trump often talks about making staff changes without following through, so those who had spoken to the President cautioned that a change may not be imminent or happen at all.
- Did Trump antagonists leak the report as a warning shot to Trump and/or Sessions that the noose is tightening? "And it seems to me that since Attorney General Sessions hasn't been terribly truthful regarding these things that it's more likely that what Kislyak was saying was the case".
At the time, Trump told reporters, "It's just not something that I feel very strongly about".
"So where is the investigation A.G.", Trump tweeted. Trump once told Clinton during the second presidential debate that she would be in jail if he were president. "Witch Hunt. Next up, 11 year old Barron Trump!"
"Problem is that the acting head of the FBI & the person in charge of the Hillary investigation, Andrew McCabe, got $700,000 from H for wife!"
Earlier that day, Trump had tweeted: "Sleazy Adam Schiff, the totally biased Congressman looking into 'Russia, ' spends all of his time on television pushing the Dem loss excuse!"
That would leave the president with another attorney general of whom he has been sharply critical in both public and private for his handling of the Russian Federation probe, according to four White House and outside advisers.
But Giuliani dismissed the report and said Sessions was right to have recused himself from the Russian Federation probe, CNN reported.
The associate reportedly replied: "If you're going to fire people at Justice, don't you want to save that bullet for Mueller?"
The facts: Sessions was the first senator to endorse Trump and served as a close campaign adviser.