Mueller is examining tweets from Trump about his Attorney General Jeff Sessions and the former FBI Director James Comey, the media reported, citing people familiar with the mater.
The special counsel is trying to determine whether any of the president's statements could qualify as attempts to obstruct the probe by intimidating witnesses or pressuring top officials, the report added.
Moreover, Mueller wants to interview Trump about his statements on Twitter, the report said.
Mueller has been leading the Russia probe for over a year after the US intelligence community concluded that Moscow attempted to sway the 2016 election in favor of Trump. Both the White House and the Kremlin have denied allegations of collusion during the 2016 campaign, with Trump calling the investigation a "witch hunt."