"Either he was lying about not having discussed that, or he forgot," Franken said told CNN's Jake Tapper on "State of the Union."
"I don't think you want a guy who'd forget that," he said.
Flynn cannot rule out that he spoke to a Russian official about sanctions, an aide close to the national security adviser said Friday.
Flynn, the aide said, has "no recollection of discussing sanctions," but added that the national security adviser "couldn't be certain that the topic never came up."
Franken also called for an investigation into Trump's business ties with Russia -- complaining that that President still has not released his personal income tax returns.
"He's got a bit of a Putin crush, and I want to know how much of that is tied maybe to financials," Franken said.
Franken said he supports an independent counsel investigating Trump, or a probe led by Sens. Lindsey Graham, R-South Carolina, and Sheldon Whitehouse, D-Rhode Island, the chair and ranking member of the Senate Judiciary Subcommittee on Crime and Terrorism.
"There's going to have to be an investigation -- an independent investigation into the Trump campaign and the Trump administration's relationship to Russia," he said. "Russia interfered in this campaign. We know that, although Trump denied it for a long time. We have not seen the President's income tax. His son said a few years ago that an inordinate amount of money was coming in from Russia investing in them."
He added: "There is a lot here that we need to look at. We need to have an independent investigation."
Franken repeatedly suggested Trump could have undisclosed business ties to Russia.
"We need something transparent and we need an investigation because we don't know what he owes Russia. We don't know how many Russian oligarchs are invested in his business. He has sidled up to Putin in so many ways," he said.
White House policy director Stephen Miller deflected questions about whether Flynn should be fired, calling it a "sensitive matter."
"It's not for me to answer hypotheticals. It wouldn't be responsible. It's a sensitive matter," he told NBC's Chuck Todd on "Meet the Press," adding that the White House "did not give me anything to say" on the issue.
"That's the question that I think you should ask the president, the question you should ask Reince (Priebus), the chief of staff," Miller said.
New Jersey Gov. Chris Christie was critical of Flynn, too, telling Tapper in a separate "State of the Union" interview that "you have one President at a time."
But Christie did not call for the White House to take any specific action to reduce Flynn's role.
"That would be up to the vice president and the President," Christie said. "And so I'm sure there will be conversations between the vice president, the President and Gen. Flynn to make sure that everybody gets the accurate story on this matter and that it's cleared up. And I think that's the obligation of Gen. Flynn."