"We will get to the truth one way or another," Lankford added.
Flynn's lawyers had previously sounded out the idea of getting immunity from prosecution in exchange for testimony before the Congress, but that was not accepted by the House and Senate Intelligence panels, which are leading the Congressional probe into Russian actions in 2016.
Flynn has come under scrutiny for several things - his contacts with Russian officials during the Trump transition, not disclosing payments from Russian groups in 2015 as required for former top military officers, and belatedly disclosing that he was working as a paid agent of the Turkish government, even as he was campaigning for Mr. Trump last year.
During the campaign, Flynn himself had raised questions about legal troubles for Hillary Clinton over her private email server, questioning why one Clinton IT aide refused to cooperate with that investigation.
"When you're given immunity, that means you probably committed a crime," Flynn told NBC's Meet the Press on September 25, 2016.