On Thursday night, his lawyer said in a statement that his client "has a story to tell" to the Capitol Hill inquisitors.
But the attorney added it would not be reasonable to submit to questioning in a "witch-hunt environment" without assurances against "unfair prosecution".
Why immunity? Anthony Zurcher, BBC News, Washington
Michael Flynn may have a "story to tell", but what it is at this point is anybody's guess.
Donald Trump's critics will probably imagine grand revelations of possible campaign contacts with Russian operatives or even the "c" word - collusion. Beyond the news reports of ongoing conversations between Flynn's lawyer and federal investigators, however, there is no firm ground for such speculation.
It's entirely possible the immunity request is nothing more than the former senior Trump adviser attempting to insulate himself from legal trouble if he were to answer detailed questions about his foreign contacts and lobbying efforts. For instance, if he actively represented overseas interests, he may have run afoul of federal disclosure rules.
There's also the chance that Flynn could be uneasy about what he told FBI agents in January, when they asked about his conversations with Russian Ambassador Sergei Kislyak.
Either of those possibilities would be of great concern to Mr Flynn, who has a six-figure military pension to preserve, but it wouldn't be the kind of political bombshell that would directly threaten Mr Trump or his administration.
Given the uncertainty of the situation, however, there's sure to be some sleepless nights ahead for the White House.
On Friday morning, President Donald Trump tweeted that his sacked former aide should ask for immunity, also arguing it was a witch hunt.
Mr Schiff said in a statement that the panel would discuss any such request with the Justice Department and the Senate Intelligence Committee.
Mr Flynn's step was "grave and momentous", he added.
The California Democrat also said: "As with any investigation - and particularly one that grows in severity and magnitude by the day - there is still much work and many more witnesses and documents to obtain before any immunity request from any witness can be considered."
Mr Flynn was forced to resign as national security adviser on 13 February for failing to disclose talks with Russian ambassador Sergei Kislyak about US sanctions on Moscow.
He also misled US Vice-President Mike Pence about the chats, which occurred before Mr Trump took office.
Russia has denied allegations it hacked emails of Democratic groups and leaked information to tip the scales in favour of Mr Trump before last November's presidential election.
But the Senate Intelligence Committee, beginning its hearings on Thursday, heard claims the Kremlin had tried to sway the vote through "propaganda on steroids".
Ranking Democrat Mark Warner also said Moscow had paid an army of more than 1,000 people to create fake anti-Hillary Clinton news stories targeting key swing states.
Critics have highlighted a comment that Mr Flynn made in an NBC interview last September in which he said: "When you get given immunity that means you've probably committed a crime."
He was talking about reports that some of Mrs Clinton's aides had been granted immunity from prosecution amid an inquiry into her emails.
At last summer's Republican party convention, Mr Flynn led chants of "lock her up" aimed at the Democratic candidate over her use of a private email server.