Flynn, 58, who was appointed by Trump as his national security adviser in January, had to resign weeks later on controversy surrounding his alleged relationship with Russia.
"Obama passed along a general caution that he believed Flynn was not suitable for such a high level post," the NBC News said, quoting an unnamed official.
This happened less than 48 hours after the November 8 general elections when Obama met Trump in his Oval Office.
During the meeting, Obama asked Trump why "would he be given this was a person who had been critical in a public way (tv, media appearances and campaigning with candidate Trump of Obama," the official said.
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The White House official said that it was worth noting that Flynn previously served in the Obama administration.
Another senior White House official said if Obama and his team were so concerned with Flynn why did not he take steps to revoke his security clearance.
Flynn, one of the early backers of Trump during his presidential run, remained in the top position of National Security Advisor for just three weeks, making him one of the shortest-serving senior presidential advisers in modern American history.
Flynn, a retired Army lieutenant general, in his resignation letter apologised to Trump and Vice President Mike Pence for briefing them with incomplete information on his talks with the Russian Ambassador before the swearing in.
Later today, former Acting Attorney General Sally Yates is scheduled to testify before a Congressional committee on Flynn.
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