The Republican leader gave the order in June 2017, according to the Times, but White House counsel Don McGahn refused, saying it would have a "catastrophic effect" on Trump's presidency. However, according to the source, McGahn did not threaten to resign directly to the President.
Sessions was the first member of Trump's Cabinet known to have been questioned by Mueller's office.
Trump last week said he did not expect to meet with Mueller.
Although Trump may want to testify, White House special counsel Ty Cobb made the case last week that attorneys don't want to expose him to a potential a "perjury trap". Because Attorney General Jeff Sessions has recused himself from all matters related to the 2016 campaign, the power to fire Mueller falls to Deputy Attorney General Rod Rosenstein.
Mueller is trying to determine if Trump's campaign advisers colluded with the Russian government to influence the 2016 presidential election, Independent.co.uk reported.
"There's been no collusion whatsoever", Trump said.
"She didn't do it under oath, but I would do it under oath, " Trump said, according to The Washington Post.
Two suspects still at large in deputy shooting
The flags will be lowered until sunset on the day of the funeral for Gumm, who had been with the sheriff's office since 2013. The Adams County Sheriff's Office said an officer died in a shooting in the area of 88th and Dawson Street Wednesday night.
The White House has repeatedly denied that Trump was looking at firing the special counsel.
"Apparently it was not clear to Flynn that this was about his personal conduct", another White House official said.
Blumenthal is also calling for the Judiciary Committee to release transcripts of its closed-door meeting with Donald Trump Jr. claiming there is potentially "explosive" evidence that Mueller's team needs to see. "It's a manifestation of the media".
After the infamous Comey Memo was written about in The New York Times, it was confirmed that Comey's friend, Columbia University Law Professor Daniel Richman played the role of middle man, delivering the goods to the newspaper, who then reported the details.
Mueller's is just one of several ongoing investigations into Russian meddling in the 2016 USA presidential election.
The Justice Department confirmed Sessions - who has downplayed the notion that Russian Federation interfered in Trump's favour in 2016 - was heard for several hours last week, suggesting special counsel Robert Mueller's probe was moving ever close to the president. There is no obstruction whatsoever.
Trump also maintained that he was "absolutely" prepared to be questioned under oath by the top investigator. "I would do it", he said, later adding, "I would do it under oath, yeah". It is unclear what prompted to Wednesday's comments.