The Associated Press and CNN have also reported that Obama discouraged Trump from appointing Flynn to the position.
The reports said Obama, who fired Flynn as head of the Defense Intelligence Agency roughly two years after appointing him to the position in 2012, warned Trump against hiring Flynn during a 90-minute conversation they had at the White House on November 10, two days after Trump's surprise election victory.
Trump and the White House have in recent days attempted to shift the blame for Flynn to the Obama administration.
Trump told Fox News on April 28 that Flynn was "already approved by the Obama administration at the highest level" when he was hired to serve as national security adviser in January. He doubled down on that claim on Monday morning, tweeting that Flynn "was given the highest security clearance by the Obama Administration - but the Fake News seldom likes talking about that."
Obama fired Flynn in 2014 amid problems with Flynn's temperament and management style.
The news of Obama's warning to Trump comes hours before former Deputy Attorney General Sally Yates is set to testify before a Senate Judiciary subcommittee about reports that she warned the White House in January about Flynn's contact with Russia's ambassador to the US, Sergey Kislyak, during the transition period.
Yates is expected to publicly confirm those reports for the first time - and deliver a rebuke to the Trump administration in the process.
"Ask Sally Yates, under oath, if she knows how classified information got into the newspapers soon after she explained it to" the White House counsel, Trump tweeted on Monday morning.
Trump, who asked for Flynn's resignation after reports surfaced that he had misled Vice President Mike Pence about his conversations with Kislyak before Trump took office, has said he was not aware that Flynn had discussed the issue of US sanctions with the Russian ambassador.
According to CNN, however, Yates plans to insist that she told the White House about Flynn's conversations with Kislyak and how he was misleading Pence and was therefore susceptible to Russian blackmail. Yates reportedly told White House counsel Don McGahn that she had "serious concerns" about Flynn. But he was not asked to resign until February 13, at least two weeks after Yates visited the White House.
The White House did not immediately respond to a request for comment.