It's one of the questions Mueller's team submitted to Trump, The New York Times reported Monday evening. The newspaper said someone outside Trump's legal team provided the list.
The Trump campaign did not respond to CNBC's request for comment.
Prior media reports have documented attempts from Russian sources to reach out to Trump's campaign. Most notably, Trump campaign officials, including Manafort and Donald Trump Jr., met Kremlin-connected lawyers in a now-infamous June 2016 meeting at Trump Tower. The Russians had promised damaging information on Trump's political opponent, Hillary Clinton.
But the question about campaign outreach to Russia flips the script, giving a new thrust to the much-debated possibility that Trump's campaign may have initiated, rather than merely accepted, contact with President Vladimir Putin's regime.
"The list of questions does seem to be a road map for what Mueller is interested in, and it's interesting from that perspective," said Michael German, a former FBI special agent and current fellow with the Brennan Center for Justice's Liberty and National Security Program.
"The questions seem formulated to solidify elements of chargeable offenses," German added in an interview with CNBC.
German cautioned, however, that Mueller's question may in fact be based on publicly available information.
Specifically, The Washington Post reported in September, citing people familiar with the discussions, that Manafort in 2016 offered to provide a Russian oligarch with Trump campaign briefings.
"If he needs private briefings we can accommodate," Manafort reportedly told an intermediary of the Kremlin-linked billionaire, Oleg Deripaska, in an email dated July 7, 2016.
No evidence surfaced that Deripaska received, or responded, to the email, the Post reported.
Trump on Tuesday criticized the Times for publishing the questions, calling the "leak" of the list of questions "disgraceful."
He also said that there were "no questions on collusion" in the list. Although the word "collusion" is not specifically used, multiple questions ask Trump to provide his knowledge of his campaign officials' contacts with Russian sources.
The White House did not respond to CNBC's request for comment.
While Trump said the "phony crime" of collusion "never existed," David Shapiro, a professor at John Jay College of Criminal Justice, said that lawyers generally stick to the "rule of thumb" of "never ask a question unless you already know the answer."
But, he added, the inclusion of the question could also be a strategic move by Mueller's team.
"There may be a sort of bluffing aspect," Shapiro said. "Lawyers are crafty folks."
According to the Times, some of the other questions were:
When did you become aware of the Trump Tower meeting?
What discussions did you have during the campaign regarding any meeting with Mr. Putin? Did you discuss it with others?
During the campaign, what did you know about Russian hacking, use of social media or other acts aimed at the campaign?
What did you know about communication between Roger Stone, his associates, Julian Assange or WikiLeaks?
What did you know during the transition about an attempt to establish back-channel communication to Russia, and Jared Kushner's efforts?