Flynn resigned as Trump's national security adviser on February 13 after only 24 days on the job.
CNN also reported that Flynn has expressed concern about the potential legal exposure of his son, Michael Flynn Jr., who, like his father, is under scrutiny by Mueller, multiple sources familiar with the matter tell CNN.
Special Counsel Robert Mueller's team are investigating a meeting between President Trump's former National Security Adviser Michael Flynn and Rep. Dana Rohrabacher (R-Calif.), who has exhibited pro-Russia views on a number of policies, according to NBC News.
Gulen, who has been living in self-imposed exile since 1999, strongly denies the accusations of involvement.
The questions were part of a criminal inquiry into Flynn's paid lobbying efforts for Turkey after he was sacked as head of the Defense Intelligence Agency and joined the Trump campaign as a senior advisor.
Additionally, three people familiar with the probe said investigators are examining whether Flynn and other participants discussed a way to free a Turkish-Iranian gold trader, Reza Zarrab, who is jailed in the U.S. Zarrab is facing federal charges that he helped Iran skirt U.S. sanctions.
The plan was to remove Muslim cleric Fethullah Gulen, an avowed enemy of Turkish leader Recep Tayyip Erdogan, from the USA and return him to Turkey.
The alleged plan emerged during the wider investigation of possible Russian interference in the 2016 presidential election and any collusion by president Trump's campaign.
A spokesman for Mueller declined to comment on the reported inquiry into a plot to seize Gulen, and Robert Kelner, a lawyer for Flynn, didn't immediately respond to a request for comment. In his resignation letter he apologized to the president for giving "incomplete information" about his interactions with the Russian ambassador to the U.S.
Mr Woolsey has previously told CNN that in September, "there was at least some strong suggestion by one or more of the Americans present at the meeting that we would be able, the United States would be able, through them, to be able to get hold of Gulen". But by mid-December Trump had named Flynn national security adviser and he was playing a central role in the transition.
It was reportedly organized by Flynn's lobbying group the Flynn Intel Group, and was also attended by Flynn's son Michael G. Flynn, as well as his business partners Bijan Kian and Brian McCauley. Flynn penned an op-ed last November suggesting the USA should expel Gulen.