The White House did not immediately respond to a request for comment on Monday.
Mr Flynn had been pushed out by Mr Obama from his job as director of the Defense Intelligence Agency during the Democratic president's term in office.
Mr Flynn has emerged as a central figure in probes into allegations of Russian meddling in the 2016 US election and possible collusion between Mr Trump's campaign and Moscow.
A former US deputy attorney general, Sally Yates, is expected to tell a Senate Judiciary subcommittee later on Monday that she had warned the White House counsel after Mr Trump took office that Mr Flynn had not told the truth about conversations he had held with Russia's ambassador to Washington.
Mr Trump fired Mr Flynn, a retired general, in February for failing to disclose talks with Ambassador Sergei Kislyak about US sanctions on Moscow and then misleading Vice President Mike Pence about the conversations.
Congressional committees began investigating after US intelligence agencies concluded that Russian President Vladimir Putin had ordered hacking of Democratic political groups to try to sway the election toward Mr Trump. Moscow has denied any such meddling.
Mr Trump has also dismissed the allegations, suggesting instead that Mr Obama might have wiretapped Trump Tower in New York or that China may have been behind the cyber-attacks. He has provided no evidence and neither scenario has been supported by intelligence agencies.
Hours before Monday's Senate hearing, Mr Trump insinuated that Ms Yates, an Obama administration appointment, had leaked information on Mr Flynn to the media.
"Ask Sally Yates, under oath, if she knows how classified information got into the newspapers soon after she explained it to WH Council," Mr Trump wrote on Twitter, apparently mis-spelling the word counsel.
In another Twitter post, Mr Trump noted that Mr Flynn had been granted top security clearance while working in the Obama administration.
James Clapper, Obama's former Director of National Intelligence, will also testify to the Senate panel on Monday. Both he and Ms Yates have left government: Mr Trump fired Ms Yates in January and Mr Clapper retired on January 20, when Mr Trump took office.