The president also has repeatedly taken to Twitter to belittle Sessions, who he calls his "beleaguered" attorney general.
Sources said if McCabe is terminated by close of business this Friday, that would mean McCabe would not receive a government pension.
"That process includes recommendations from career employees and no termination decision is final until the conclusion of that process", she said in a statement. "We have no personnel announcements at this time".
Justice Department Inspector General Michael Horowitz has for some time been working on a report that blasts McCabe for allowing two high-ranking bureau officials to sit down with the Wall Street Journal as the news outlet prepared a story in 2016 on an investigation into Hillary Clinton's family foundation, then misleading the inspector general's team about his actions.
Trump's statements about McCabe put pressure on Sessions to fire him, and would create an appearance of impropriety even if Sessions' decision to fire McCabe were backed by a formal recommendation.
McCabe is a 21-year bureau veteran, and would be the first deputy director to be fired. A government official at the time said Mr. McCabe was merely using his retirement eligibility a few weeks early.
Republicans have questioned McCabe's ties to the Democratic Party, considering his wife ran as a Democrat for a Virginia Senate seat in 2015 and got financial help from a group tied to Clinton family ally Terry McAuliffe.
"FBI Deputy Director Andrew McCabe is racing the clock to retire with full benefits", Trump tweeted in December. Trump asked previous year.
The issue stems from findings in an internal Justice Department watchdog report that claims he misled investigators about his decision to authorize FBI officials to speak to the media about an investigation into the Clinton Foundation.
While Trump has suggested that McCabe was a Clinton supporter, the justification for firing him ― ironically ― has to do with a decision he made that was damaging to Clinton and Obama appointees in the Justice Department.
That report, which has been complete for over a week, according to the source, has not been released publicly.