Mike Flynn arrives for a news conference February 13, 2017, in the East Room of the White House in Washington.
"I don't have sufficient information to make a determination about whether or not such cooperation or complicity or collusion was taking place", Brennan said.
Responding to the subpoena, Kelner's letter to Burr and Warner claims Flynn was eager to "give a full account of the facts".
Former CIA chief Brennan's testimony to the House intelligence committee was the clearest public indication yet of the significance the Russian Federation contacts play in counterintelligence investigations that continue to hang over the White House. After the firm's deduction, Flynn received the $33,000, according to records obtained by the committee. Earlier this month, Trump fired the Federal Bureau of Investigation director, James Comey.
The probe appears to be reaching close to President Donald Trump and his inner circle.
Sen. Dianne Feinstein, a member of the intelligence committee, said she also plans to press Comey regarding what was discussed with Trump about Flynn and whether he was asked by Trump to alter the FBI investigation.
During the Oval Office chat, which U.S. media were not invited to cover, Mr Trump also reportedly divulged secret information on the military campaign against so-called Islamic State.
Hours later, Rep. Elijah Cummings, senior Democrat on the House oversight committee, said government documents he's reviewed showed inconsistencies in Flynn's disclosures to US investigators in early 2016 during his security clearance review.
"It is hard to understand how General Flynn could have believed that his dinner with Russian President Vladimir Putin was 'insubstantial contact, '" Cummings wrote. Cummings' letter came the same day Flynn declined to provide documents to the Senate Intelligence Committee, citing his Fifth Amendment protection from self-incrimination.
Referring to the whole sequence of events leading to Comey's firing, Cummings said: "I think that there may be quite a few people that may have some problems with the law".
He had wrongly informed Mr Pence that he had not discussed United States sanctions on Russian Federation that were imposed as punishment for meddling in the 2016 election.
Legal experts also pointed out that if Flynn is granted immunity from criminal prosecution, then he would no longer have Fifth Amendment rights against self-incrimination and could be compelled to answer all questions and release all documents.
Two other former Trump associates - one-time campaign chairman Paul Manafort and Republican operative Roger Stone - have turned over documents the Senate panel had requested, while a third - campaign adviser Carter Page - had not yet complied, NBC News reported, citing a congressional source.
Flynn invoked the Fifth Amendment and rejected the committee's subpoena request for documents relating to Russian interference in the 2016 presidential election earlier this week.
An additional complication for the congressional committees: If they move to grant Flynn immunity, they will likely have to enter into discussions with Mueller to determine whether that could impede the FBI's case.
It is the only subpoena the committee has issued in the course of its investigation into Russian involvement in the 2016 election, a probe that includes delving into any contacts the Trump campaign and transition teams may have had with Kremlin officials.