The Special Counsel is looking into messages the President has posted about former FBI director James Comey, and Attorney General Jeff Sessions.
According to the New York Times, Mr Mueller wants to question Trump about the tweets, and is also looking into apparent false statements made by the White House.
There could also be probing into Trump’s private meetings with Mr Comey and Mr Sessions.
Lawyers are apparently looking into specific tweets from key moments in Trump’s premiership. It is thought these could be some of them.
A year ago, Trump criticised Sessions as “weak” for not investigating Hilary Clinton’s “crimes”.
Reports have indicated Trump wanted to fire Sessions but was ultimately convinced not to.
But, Trump has often claimed he would never have hired the former senator had he known Mr Sessions would recuse himself from the Russian investigation.
In October, Trump used the social media site to slam Mr Comey.
Mr Comey has often come under fire from the President.
During testimony last year, the President asked the lawyer if he could “let go” of former national security adviser Michael Flynn as the Russia investigation continued.
Twelve days after the tweets, Mr Mueller announced charges in the Russia investigation against former Trump campaign manager Paul Manafort and adviser Rick Gates.
Trump’s team have denied any wrongdoing.
His personal lawyer, Rudy Giuliani, told the New York Times: “If you’re going to obstruct justice, you do it quietly and secretly, not in public.”