Mr Obama warned his successor less than 48 hours after the November election during a conversation in the Oval Office, former Obama officials said.
Mr Flynn's contacts with a Russian envoy left him vulnerable to blackmail, a Senate panel heard on Monday.
He was fired in February for concealing the nature of these contacts.
Mr Flynn, a retired army lieutenant-general, misled the Trump administration about discussing US sanctions against Russia with the country's envoy, Sergei Kislyak, before the inauguration.