"Do you think we're gathering compromising information on all of them right now or something?"Putin asked, before saying: "Have you all lost your senses?"
Mr Putin also said it was "nuts" to suggest the Trump administration had moved to ease economic sanctions on Russian Federation.
Flynn, a retired lieutenant general, briefly served as an adviser to Trump's campaign and later as the president's national security adviser.
Putin on Sunday also denied the existence of a dossier of dirty secrets gathered on President Donald Trump.
John Oliver's Last Week Tonight isn't the only TV program to focus on Vladimir Putin, but is probably the only one to call the Russian ruler "perhaps the biggest threat to the United States after the President of the United States". "So, if this theory is correct, and that can't be ruled out, then what could be easier in this day and age than using all the technical means at the disposal of the intelligence services and using those means to organize some attacks and then pointing the finger at Russian Federation?" he said.
A member of the Senate intelligence committee says "we've seen no smoking gun at this point" regarding collusion between the Trump campaign and the Russian government during the 2016 USA presidential election.
According to the American journalist, following her professional encounter with the Russian leader she can describe Putin as a "very gracious" person, at least off camera. He said, as quoted by NBC, "Put your finger anywhere on a map of the world, and everywhere you will hear complaints that American officials are interfering in internal electoral processes".
He said they met at a dinner in Moscow in December 2015 and he was told only afterwards that Flynn was formerly in the security services.
She'll try out the Oprah bit next Sunday whens she interviews sportscaster Erin Andrews.
It was always doubtful Putin, a former KGB agent and spin master, would do anything but rebuke accusations of Russian involvement.
On the alleged connections with Donald Trump's people and accusations of interference with U.S. elections had been "selected by someone as a line of attack against the current [US] president", Putin told the NBC host.
"There wasn't anything to talk about", Putin said through an interpreter. "You people over there ... good job. That's the extent of my acquaintance with Mr Flynn", he added.
"I hadn't said anything". "And such situations do occur in the history of the United States". "Who is talking? Who is taking offense that we are interfering?"
Step by step, Putin dismantled the assumptions behind the liberal narrative that Donald Trump had close connections with Russian Federation, and that Putin has leverage over the president. Do you think I have the time to talk to our ambassadors all over the world every day?