The New York Times reported on Tuesday that two people briefed on a letter from Mueller's office to the White House, sent on Friday, signaled the prosecutor's willingness to accept written responses from Trump on the issue of alleged collusion.
Mueller himself has not made any such allegations, however when he was granted control of the FBI's counterintelligence investigation it was under the mandate that he probe "any links and/or coordination bet ween the Russian government and individuals associated with the campaign of President Donald Trump; and any matters that arose or may arise directly from the investigation."
The special counsel may still seek an interview with the president on whether he obstructed justice by somehow hindering the investigation, presumably by firing former FBI Director James Comey.
According to the Times, Mueller's team believes that "issues of executive privilege" could hamper their quest for an in-person meeting on the obstruction allegation.
Trump's team reportedly reacted to the letter with pleasure, believing it to indicate that the scope of a Trump-Mueller interview would be therefore curtailed from what they were originally expecting.
The written interview, if it is in fact eventually conducted, would follow interviews between senior White House aides and Trump administration officials. The administration has also turned over more than 1.4 million documents in in compliance with the probe.
Trump has repeatedly denied that any collusion occurred between his campaign and the Kremlin. On August 23, he tweeted simply "NO COLLUSION — RIGGED WITCH HUNT!"
So far, the special counsel has indicted a number of Russians, alleging that they interfered with the 2016 presidential election, including supposed Russian intelligence operatives (although Moscow says they are not) over allegedly hacking the Democratic National Committee, and other Russian nationals accused of spreading memes and events on social media, although coordination has not been alleged. Former Trump campaign manager Paul Manafort was found guilty as a result of the investigation, and former longtime Trump lawyer Michael Cohen pleaded guilty, in August to charges unrelated to collusion.