He 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.
White House press secretary Sean Spicer told the daily briefing on Monday: "It's true that President Obama made it known that he wasn't exactly a fan of General Flynn's."
But Mr Spicer said that should not come as a surprise "given that General Flynn had worked for President Obama [and] was an outspoken critic of President Obama's shortcomings specifically as it related to his lack of strategy confronting Isis and other threats around that were facing America".
The Obama administration fired Mr Flynn from his role as head of the Defense Intelligence Agency in 2014, citing issues of mismanagement and temperament.
Mr Obama's warning to Mr Trump 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.
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