Flynn attorney Robert Kelner declined comment.
Chairman Sen. Richard Burr, R-North Carolina, and Vice Chairman Sen.
Flynn has previously sought immunity, a request backed by Trump in a tweet.
The development comes a day after United States President Donald Trump, in a bid to sweep away the man who is responsible for an investigation into whether members of his campaign team colluded with Russian Federation in its interference in last year's elections, fired FBI director James Comey.
Flynn was sacked by Trump in February after published reports that the national security adviser had misled Vice President Pence about his discussions with the Russian ambassador to the United States.
Page has already replied to the committee numerous times, saying he will not cooperate with their request until Senate investigators ask former President Barack Obama's administration for his communications - an allusion to Page's accusation that he was targeted by the Obama administration.
He also says in an appearance on NBC's "Today" show that he favored the firing of FBI Director James Comey and thought that Trump "made the right decision". Multiple intelligence leaks and news reports have confirmed all had contacts with Russian government officials during Trump's campaign.
Earlier this week, former acting Attorney General Sally Yates told a separate Senate panel that she was so troubled that Flynn had misled Vice President Mike Pence about his December conversations with the Russian ambassador that she warned the White House counsel that Flynn was vulnerable to blackmail and could even face criminal charges.
Flynn's lawyer did not immediately respond to questions from Newsweek about whether Flynn plans to respond to the legal order and how many documents he has relating to the investigation.