By Maegan Vazquez, CNN

(CNN) -- President Donald Trump said Thursday that if he wanted to fire special counsel Robert Mueller, he would have months ago.

"If I wanted to fire Robert Mueller in December, as reported by the Failing New York Times, I would have fired him. Just more Fake News from a biased newspaper," Trump tweeted Thursday morning.

Trump was disputing a New York Times report published Tuesday that said the President sought to fire Mueller in December following reports that Mueller was seeking Trump's financial records. CNN has also reported that Trump has wanted to fire Mueller for months.

Later Thursday afternoon, the President tweeted about the Mueller investigation again, this time saying he "agreed with the historically cooperative, disciplined approach that we have engaged in with Robert Mueller (Unlike the Clintons!)."

"I have full confidence in Ty Cobb, my Special Counsel, and have been fully advised throughout each phase of this process," he continued.

The legality of firing Mueller has been a topic of conversation inside the White House since the indictments of former Trump campaign chairman Paul Manafort and his deputy, Rick Gates, last fall, a source told CNN.

White House press secretary Sarah Sanders said Tuesday that the President "certainly believes he has the power" to fire him.

On Tuesday, CNN also reported that Trump is considering firing Deputy Attorney General Rod Rosenstein, who oversees the Mueller probe.

The news of potential DOJ firings comes following a raid on the office and hotel room of Michael Cohen, the President's personal attorney and confidante. Referred by Mueller to seek a search warrant, authorities sought information that included payments allegedly made to keep women silent about affairs with Trump more than a decade ago.

Some of Trump's legal advisers have told him that their team now has a stronger case in firing Rosenstein because believe he crossed the line in what he can and cannot pursue with the raid, CNN reported Tuesday.

A White House official said earlier this week that Trump and his legal team are re-evaluating whether the President should sit down for an interview with Mueller's team in light of the raid.