Trump's ex-national security advisor, whose links to Russia are one focus of the sprawling investigation, has sought protection in exchange for his testimony to the FBI and congressional committees.
Flynn's lawyer said in a statement Thursday that his client has "a story to tell, and he very much wants to tell it, should the circumstances permit."
But two key committees in the probe, the House and Senate Intelligence Committees, both suggested the immunity proposal was premature.
Trump nevertheless encouraged Flynn's move in a tweet that appeared to lay down a challenge.
"Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!"
Flynn's offer to testify under protection from prosecution suggests he has more to reveal about the Russia affair.
He could be a key witness as the Federal Bureau of Investigation and Congress seek to determine whether Trump advisors colluded with Russia's interference in last year's presidential election.
But Adam Schiff, the senior Democrat on the House panel, said there was "still much work and many more witnesses and documents to obtain before any immunity request from any witness can be considered."
"We should first acknowledge what a grave and momentous step it is for a former national security advisor to the president of the United States to ask for immunity from prosecution," Schiff said.
NBC News also quoted unnamed officials as saying the issue was not on the table at the Senate committee "at the moment."
Close Trump advisor
A close advisor to Trump's 2016 campaign, Flynn was forced to step down from his White House job in February after misleading the vice president about conversations he had with Russian Ambassador Sergey Kislyak after the election.
He is also in focus over receiving $33,000 from Russian television RT to attend a 2015 gala in Moscow where he sat with Russian President Vladimir Putin, and $530,000 from Turkey for lobbying services.
But Flynn is not the only member of Trump's advisors to have had contacts with Russia during the campaign. Investigators want to know whether there was any collusion between them and Moscow's concerted effort last year to hurt Trump's Democratic election rival Hillary Clinton.
What Flynn could tell investigators is unknown. US prosecutors can offer a suspect immunity in exchange for information that can incriminate others in a case, particularly larger figures.
Asking for immunity, said criminal lawyer Mark Bennett on Twitter, is "a reasonable stance for someone to take even if she hasn't done anything wrong -- especially where... the grand jury's investigation appears to have political overtones."
Alex Whiting, a Harvard Law School professor writing on the Just Security website, said Flynn's offer to testify in exchange for immunity was "not a serious offer," suggesting it was rather a tactical move.
A real offer to the FBI would never have gone public in this way, he noted, given that it would have to involve Flynn negotiating to provide very serious evidence against powerful figures, including possibly the president.
"The fact that Flynn and his lawyer have made his offer publicly suggests that he has nothing good to give the prosecutors."
Instead, he said, it was more likely an effort by Flynn to protect himself from Justice Department prosecution, by first obtaining immunity from one of the bodies in Congress probing the Russia affair.
Conceivably, one of the Republican-dominated committees could do that to protect Flynn.
Critics assailed the president over his tweet, noting that during last year's campaign, Trump said in a speech that "If you're not guilty of a crime, what do you need immunity for?"
Asked by journalists Friday if Trump though Flynn was guilty of something, White House spokesman Sean Spicer said the president just wants Flynn to testify.
"He thinks Mike Flynn should go testify and do what he has to do to get the story out," Spicer said.