Flynn proposed his deal to the Federal Bureau of Investigation and the House and Senate intelligence committees, The Wall Street Journal reported late yesterday.
A close advisor of Trump's 2016 campaign, Flynn was forced to step down just weeks into the security job last month.
His resignation came after it emerged that he made misleading statements about talks he held with Russian Ambassador Sergey Kislyak during the presidential transition concerning Washington's sanctions on Moscow.
The Journal said it wasn't clear what exactly Flynn had offered to discuss.
But it quoted one unnamed official as saying the retired army general's bid for immunity suggested potential "legal jeopardy" for him.
Robert Kelner, a lawyer for Flynn, said in a statement tweeted late yesterday that "General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit.
The New York Times quoted a congressional official as saying investigators are wary of cutting a deal with Flynn until they are further along in their probe and have a better idea of what information Flynn might offer.
The Times also quoted an expert as urging caution over Flynn's offer of testimony.
"At this early stage, I wouldn't read anything into this request beyond smart lawyering," Mark Zaid, a Washington lawyer specialising in national security cases, was quoting as saying by the Times.
"I would suspect both Congress and the FBI will first generate additional evidence from smaller players before deciding to immunise General Flynn," Zaid said, according to the Times.
At least four investigations are under way into allegations that Moscow tried to swing November's presidential election in Trump's favour, as questions swirl about whether some in the Republican's inner circle colluded with Russia.
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