Prosecutors working for Mr Mueller filed court documents recommending a jail sentence for George Papadopoulos, a former Trump campaign foreign policy adviser.
The Mueller court documents said Mr Papadopoulos caused irreparable damage to the Russian Federation investigation because he lied repeatedly to agents during a January 2017 interview.
Mueller's team says in a new court filing that George Papadopoulos should spend at least some time incarcerated and pay a almost $10,000 fine.
"The government does not take a position with respect to a particular sentence to be imposed, but respectfully submits that a sentence of incarceration, within the applicable guidelines range of 0 to 6 months' imprisonment, is appropriate and warranted", Mueller wrote on Friday in a government sentencing memorandum to the US District Court for the District of Columbia.More news: Manchester United's Alexis Sanchez misses Brighton clash through injury
To make matters worse for Papadopoulos, the prosecutors say he has not provided significant help in their investigation.
Papadopoulos will be sentenced on September 7.
Friday's 10-page filing provided fresh details of how Papadopoulos' lies impeded the Federal Bureau of Investigation, according to prosecutors, who went on to say his lack of cooperation justified a prison term.
Mifsud was not named in the court filing Friday night, but CNN learned the name of the mysterious "Professor" after Papadopoulos' guilty plea became public a year ago.More news: Kofi Annan, former United Nations secretary-general, dies at age 80
The FBI located the professor in Washington about two weeks after Papadopoulos' initial January 27, 2017, interview with Mueller's investigators, but the professor left the country on February 11, 2017, and has not returned to the United States, prosecutors said. Last October, Papadopoulos pleaded guilty to charges of lying to the Federal Bureau of Investigation regarding his contacts with Russian operatives during the Trump campaign - including at least one meeting where he was offered thousands of emails meant to damage Hillary Clinton's campaign.
While drinking at a London bar in May 2016, he told the Australian ambassador to Great Britain that the Russians had hacked thousands of emails that could damage Clinton's presidential campaign.
Prosecutors note that investigators also missed an opportunity to interview others about the professor's comments or anyone else at that time who might have known about Russian efforts to obtain derogatory information on Clinton during the campaign.
The recommended sentence of zero to six months matches what Mueller's team already agreed to suggest to the judge in this case. Most immediately, those statements substantially hindered investigators' ability to effectively question the Professor when the Federal Bureau of Investigation located him in Washington, D.C. approximately two weeks after the defendant's January 27, 2017 interview. The Australians passed the information to the United States and, in July 2016, the FBI opened its investigation into links between the Trump campaign and Russian Federation. Papadopoulos said wrongly several times he had communicated with Mifsud before he joined the Trump campaign. The probe was later taken over by Mueller.More news: Kevin Love on why he thinks LeBron James left Cavs for Lakers