Mr Flynn's contacts with a Russian ambassador are expected to come up in a Senate hearing 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.
When Mr Trump sat down with Mr Obama just two days after winning the election last November, it was smiles all around. Now, according to reports, it turns out Mr Obama spent part of the time warning him to steer clear of Michael Flynn - and the president-elect ignored his advice.
In hindsight, Mr Trump would have been better served heeding his predecessor's advice, as the ensuing scandal over contacts with Russian Ambassador Sergey Kislyak quickly ended Flynn's controversial tenure as the president's national security advisor.
The timing of this revelation, just hours before Sally Yates is set to testify Mr Flynn's Russian ties and her own efforts to warn the Trump administration, is no fluke.
The president took a shot at the woman he fired as acting attorney general via Twitter this morning, and now Mr Obama's team is coming - anonymously - to her defence.
It's yet the latest bit of evidence of an ongoing feud between the past and present presidential administrations as well as the tension between Mr Trump's inner circle and the US intelligence community.
The stakes are high, and there's no indication anyone is backing down.
But on Monday, Mr Spicer questioned the former president's objections to Mr Flynn.
"If Mr Obama was truly concerned about General Flynn," the White House press secretary told reporters, "why didn't he suspend General Flynn's security clearance, which they had just reapproved months earlier?
"Additionally, why did the Obama administration let Flynn go to Russia for a paid speaking engagement and receive a fee?"
The revelation came as former acting Attorney General Sally Yates testified 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.
What happened to Flynn and when
- April 2014 - fired as director of the DIA under Obama
- Dec 2015 - attends dinner in Moscow as paid speaker
- Feb 2016 - begins work on Trump campaign
- 10 Nov 2016 - Obama warns Trump not to recruit Flynn
18 Nov 2016 - accepts job offer of national security adviser
- Dec 2016 - speaks to Russian ambassador
- Late Jan 2017 - acting deputy attorney general warns White House that Flynn spoke to ambassador
- 8 Feb 2017 - denies discussing sanctions with ambassador
- 13 Feb 2017 - resigns as national security adviser
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