Last week the committee's chairman Senator Richard Burr told reporters that Mr Flynn was "not cooperating" with the investigation, adding that they had not received "a definitive answer" on whether he would testify.
Separately on Monday, the Washington Post reported that Trump asked two of the country's top intelligence officials, Director of National Intelligence Dan Coats and National Security Agency Director Admiral Michael Rogers, to help him deny any collusion between his team and Russian Federation during his presidential campaign. The FBI is also investigating.
Adding to his woes, a Democratic lawmaker said Monday that Flynn may have lied to federal investigators when he told the Pentagon during a security review that he was paid $33,750 by a USA company for making a speech in Moscow in December 2015, shortly before he began advising Trump's presidential campaign.
In the letter, Cummings states documents in the panel's possession show Flynn received $45,000 to speak at a conference that was paid for by a Russian media company as well as airfare and lodging for Flynn and his son.
Flynn told investigators that "U.S. companies" had paid for the trip, but the committee has documentation that Russian state-run media outlet RT funded the trip, the letter said.
Attorneys for Michael Flynn say that a daily "escalating public frenzy against him" and the Justice Department's appointment of a special counsel have created a legally unsafe environment for him to cooperate with a Senate investigation.
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The Senate Intelligence Committee had requested Mr Flynn provide a list of all meetings and communications he had with Russian officials from January 16, 2015 through to January 20, 2017.
Mr. Brennan's testimony before the House intelligence committee on Tuesday comes one day after Mr. Flynn invoked his constitutional right against self-incrimination in response to a subpoena from the Senate intelligence committee.
But Flynn is expected to send a letter later Monday invoking his Fifth Amendment rights.
"He is the target on almost a daily basis of outrageous allegations, often attributed to anonymous sources in Congress or elsewhere in the United States government".
Lawyers for Michael Flynn said they felt his testimony to the probe would likely be used against him. Mark Warner said, "We have to find out whether we have the ability to either hold Gen. Flynn in contempt or whether it's just Fifth Amendment".
That's according to a person with direct knowledge of the matter. If the intelligence committee wants to give Flynn immunity, it will likely have to enter into discussions with Mueller to determine whether the move could impede the FBI's case. He previously had offered to testify to Congress in exchange for immunity from prosecution, a request lawmakers spurned.