Will President Trump push out Jeff Sessions?

NEW YORK (FOX 5 NEWS) - The president is continuing to make digs at Attorney General Jeff Sessions. So speculation is growing about who might replace him. Sen. Ted Cruz, Trump's former nemesis during the campaign, is a top contender, the Washington Post reported. Trump called him "Lyin' Ted" during the Republican primaries.

The Post article also named former New York Mayor Rudy Giuliani. And New Jersey Gov. Chris Christie is still another name bantered around.

But Iona College Professor Jeanne Zaino said Giuliani and Christie have too much negative baggage to survive the Senate confirmation process.

"If Jeff Sessions does resign, I don't see those two as being viable options," Zaino said.

Giuliani shot down the idea that he had been approached to replace Sessions. He also said he doesn't want the job and if he would've been in Sessions' position, he would've recused himself from the Russia probe as well.

The president is fueling speculation about Sessions' demise. In a tweet, Trump referred to Sessions as the "beleaguered AG." The president's dissatisfaction with Sessions for recusing himself from the Russia investigation has apparently reached a tipping point.

But it is widely known the president does not like to fire people, so he could use other tactics.

Trump is "making it uncomfortable for him to stay around and perhaps hoping that Attorney General Sessions will decide to leave the office under his own steam," Baruch College Dean David Birdsell said.

When asked about the president's plans for Sessions, new White House communications director Anthony Scaramucci told reporters on Air Force One "they need to speak and determine what the future of the relationship is."

But Trump advisor Newt Gingrich said on Fox News that replacing Sessions would be a mistake. Sessions was the first senator to support Trump's campaign when everyone else was running in the other direction.

"Loyalty is a two-way street," Gingrich said. "There's a point here where people have to say, 'The guy was with you from the very beginning and he makes one big mistake -- do you really dump him and if he you do what signal do you send to everybody else on the team?"