In a series of tweets, the president said many of his previous staffers had asked him why they had not been interviewed by the special counsel. Trump asked whether Mueller would include statements from them in a final report.
"So many campaign workers, people inside from the beginning, ask me why they have not been called (they want to be)," Trump wrote without providing names of any of those staffers. "There was NO Collusion & Mueller knows it!"
Multiple outlets have reported that Mueller's team has begun drafting a final report. That report is not required to be made public. The president's legal team said it had submitted answers to written questions from the special counsel on Tuesday, following months of negotiations.
The White House and the president's campaign did not respond to a request for comment. Peter Carr, the spokesman for the special counsel, declined to comment.
The call for Mueller to interview individuals who did not meet with Russians during the campaign appears to be a novel defense.
The strategy, however, is consistent with the Trump's handling of other aspects of his presidency, said Matthew Felling, a veteran political communications strategist and former communications director to Sen. Lisa Murkowski, R-Alaska.
"It's worked for him as a political tactic and as a foreign relations position, and now the President is tripling-down on 'Whataboutism' as a legal stance," Felling said in an email. "Basically he's like a football coach asking the referee 'What about the 10 players on the field that didn't commit a penalty on that play?'"
It is not clear how many of the president's former staffers have not met with Russian officials. The president's campaign had fewer than 100 individuals on its payroll at the height of its efforts in 2016. Many of those connected to the campaign were independent contractors, however, and were not included in its official payroll numbers.
It is also unclear if any of these former staffers have reached out to the White House, or to the special counsel requesting interviews, as Trump suggests.
Deputy Attorney General Rod Rosenstein appointed Mueller in May 2017 to lead an investigation into any links between the president's campaign and the Russian government.
To date, Mueller has filed more than 100 criminal charges against 32 individuals, including the president's former campaign chairman Paul Manafort and three former campaign advisors.
In 2016, senior campaign officials, including the president's eldest son, Donald Jr., met at Trump Tower with a lawyer with ties to the Russian government. The meeting came after the campaign was promised dirt on Trump's rival Hillary Clinton.
The campaign's foreign policy advisor, Carter Page, told lawmakers last year that during a 2016 trip to Moscow, he met with senior Russian officials including the then-deputy prime minister and a senior aide to Rosneft CEO Igor Sechin. He said the conversations were not substantive.
Also that year, at key events in Washington, Cleveland and New York, Russian operatives were reported to have been among Trump's VIP guests.
George Papadopoulos, a former campaign advisor, pleaded guilty last fall to lying to the FBI about conversations he had with people he believed were working for the Russians. He began his two week sentence on Monday.
The president has sought to discredit Mueller's inquiry. He has labeled it an "illegally brought Rigged Witch Hunt run by people who are totally corrupt and/or conflicted."
Last year, the president ordered then-White House Counsel Donald McGahn to fire Mueller, The New York Times reported. The president backed down after McGahn threatened to resign.
— CNBC's Christina Wilkie contributed to this report.