During an interview Friday on Fox News' "The Ingraham Angle", Mukasey said Obama wanted Comey to let Clinton "off" the hook because Obama believed, "if you wind up accusing her, you wind up accusing me".
Flynn had been fired in February of 2017 after White House officials said he had misled them about his Russian contacts during the transition period.
The two officials bonded over the idea of a proposed leak crackdown, even sharing a chuckle over a crude joke involving jailed journalists, according to memos maintained by Comey and obtained by The Associated Press. "In this case I think they have got it horribly wrong", he said of the inspector general's report on McCabe.
Responding to the claims about Russian prostitutes, Dmitry Peskov, Mr Putin's spokesman, said: "President Putin could not have said that, and did not say that, to President Trump".
The Comey memos, obtained by CNN, recount Trump's "serious reservations" about then-national security adviser Michael Flynn, Trump's concerns about media leaks, and Trump's recollection of Russian President Vladimir Putin telling him that Russia had the "most handsome hookers in the world".
On Thursday, Mr. Trump said the memos showed that there was "NO COLLUSION and NO OBSTRUCTION".
The Comey memos were written before his firing, which led to the appointment of Special Counsel Robert Mueller to continue the investigation.
It was a subject Mr Trump returned to a couple of weeks later over an intimate dinner alone with Mr Comey in the Green Room of the White House - again, captured in granular detail by another of Mr Comey's memos.
"Referral of Comey due to transmitting classified info was justified and this IG action is probably just the beginning", Republican Florida Rep. Ron DeSantis wrote on Twitter after news broke Friday that the Department of Justice's inspector general is investigating the memos' classification issues.
Opposition move to impeach CJI, Jaitley calls it 'revenge petition'
The Opposition parties at a hurriedly called Press conference announced and cited reasons for the impeachment motion. The "Institution Disrupters" have now become spokespersons of the Judge Loya death case falsehood, " he wrote.
Mr Flynn has since pleaded guilty to lying to the Federal Bureau of Investigation about those conversations and is cooperating with investigators.
They detail the president's alleged demands for loyalty from the former director and his requests for Comey to shut down its investigation into former national security adviser Michael Flynn. On April 19, the Department of Justice released them all - 15 total - to congressional leaders and they are all now public, albeit with certain words redacted.
"This isn't [redacted] we are talking about", Trump said, according to Comey.
In the memo the identity of the first leader to call Mr Trump was blacked out as classified, but officials have now confirmed that it was Mr Putin.
A flood of developments related to the Russian Federation investigation on Thursday marked the latest news-packed day in Donald Trump's presidency.
"I honestly never thought these words would come out of my mouth, but I don't know whether the current president of the United States was with prostitutes peeing on each other in Moscow in 2013", Comey told ABC.
Comey's book is nothing more than a standard swamp product.