Trump has repeatedly attacked Sessions for recusing himself from the investigation into Russian interference in the 2016 US presidential election campaign.
The attorney general, DiGenova argued, has "told people that he doesn't believe that people at the Department of Justice and the Federal Bureau of Investigation are capable of the kinds of things they are being accused of", referring to the Clinton and Russian Federation probes.
President Trump declined to answer whether he would allow Sessions to remain in the position following the midterms.
"I view it differently".
Graham also said he would offer Trump some advice: Act more like McCain. Overall, 75 percent of Democrats oppose Sessions' firing, while just 14 percent support Sessions' removal.
They want someone who'll also name a special counsel to aggressively prosecute Hillary Clinton for destroying her emails, or to fully investigate the political corruption we've learned thrived at the top of the Obama administration's Federal Bureau of Investigation and intelligence agencies.
Trump has also upped his rhetoric against the Mueller probe, which he has already branded a "hoax" and a 'witch hunt'.
Graham seemed to have Sessions' back for much of the first year of his time in the Department of Justice, but now even he is suggesting that it's time for President Trump to put someone new in the job. He's spent the last week chatting with "any senator who will listen" about how angry he is at Sessions, one Republican Senate aide said - including Sen. Rather, both McConnell and House Speaker Paul D. Ryan have said no congressional action is necessary to ensure Mueller's investigation continues because Trump wouldn't dare try to stop it. But now the attorneys are becoming convinced Mueller will try to make the case regardless of what Trump decides to do with Sessions.
White House counselor Kellyanne Conway said at the White House Thursday that Trump will make the announcement about McGahn's successor.
"I'd love to have him look at the other side ..."
Former Deputy Assistant Attorney General Marty Lederman said these are probably the biggest questions when it comes to whether Trump can actually affect the course of the investigations he faces.
"You've got a lot of people you think are treating you unfairly".