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 ambassador are expected to come up in a Senate hearing on Monday.
He was fired as national security adviser for concealing these contacts.
Mr Flynn, a retired army lieutenant-general, misled the Trump administration about discussing US sanctions against Russia with the country's ambassador, Sergei Kislyak, before the inauguration. He was fired in February.
A Senior White House official confirmed to NBC News that Mr Obama "made the president aware he was not a fan of Michael Flynn", but pointed out that the retired general had been critical of the Obama administration.
The Obama administration fired Mr Flynn from his role as the head of the Defense Intelligence Agency in 2014, mostly due to mismanagement and temperament issues.
Mr Obama's warning came before concerns emerged about Mr Flynn's contacts with the Russian ambassador, a former Obama official told NBC News.
The Democratic president reportedly thought Mr Flynn was not suited for such a high-level position.
The revelation comes the same day former acting Attorney General Sally Yates is expected to testify for the first time in public before a Senate panel about Mr Flynn's contacts with Mr Kislyak.
His links to Russia are being scrutinised by the FBI and the House and Senate Intelligence Committees, as part of wider investigations into claims Moscow sought to tip the election in favour of Mr Trump, and into contacts between Russia and members of the president's campaign team.
Ms Yates, a 27-year Justice Department prosecutor, was fired in January by Mr Trump for refusing to uphold the administration's travel ban.
President Trump on Monday appeared to accuse Ms Yates of leaking information to media on Twitter.
He also pointed out that Mr Flynn was "given the highest security clearance by the Obama administration".
"But the Fake News seldom likes talking about that", he tweeted.