Flynn was sacked as Trump's national security adviser after 24 days over misleading Vice President Mike Pence over conversations with Sergey Kislak, Russia's US ambassador.
According to the report, Flynn and his son would have been paid $15 million for bringing Fethullah Gulen to the Turkish government.
President Trump's former National Security Adviser Michael Flynn is accused of plotting to forcibly remove a Muslim cleric living in the US and delivering him to Turkey in exchange for millions of dollars.
Gulen, who has been living in self-imposed exile since 1999, strongly denies the accusations of involvement.
The Journal reported the Federal Bureau of Investigation questioned at least four people in regards to a mid-December meeting in NY at the "21" Club.
Flynn - who was forced out of his White House job this year after revelations that he had misled officials about his conversations with the Russian ambassador - reportedly discussed the plan with Turkish government representatives last December.
Rep. Devin Nunes, the chairman of the House Intelligence Committee, attended a breakfast meeting where Michael Flynn and Turkey's foreign minister were also present.
"One person familiar with the alleged discussions about Mr. Gulen said Mr. Flynn also was prepared to use his influence in the White House to further the legal extradition of the cleric, who lives in Pennsylvania", WSJ added.
President Recep Tayyip Erdogan has long sought for the U.S.to extradite Gulen, who resides in the United States. In addition to founding and working for Flynn Intel Group, he joined his father on a trip to Moscow in December 2015 during which Flynn was paid $34,000 to speak at an event celebrating the state-sponsored news agency RT, NBC News reported.
Lawyers for Flynn and his son declined to comment to the Journal.
The probe into the alleged Gulen plot is part of Mueller's larger investigation into alleged improper contacts between Trump representatives and agents of the Russian government during and after the 2016 US presidential election.
Flynn was a senior adviser on national security matters to the Trump campaign at the time, though he was also on a foreign government's payroll.
"The claim made by Mr. Woolsey that General Flynn, or anyone else in attendance, discussed physical removal of Mr. Gulen from the United States during a meeting with Turkish officials in NY is false", Flynn spokesman Price Floyd said in a statement at the time. The Daily Caller has reported that Flynn was contacted by DOJ's National Security Division on November 30.
In March, Flynn registered as a foreign agent and revealed that his company, Flynn Intel Group Inc., received $530,000 during the later months of the election to lobby the US government on behalf of Turkey. Flynn then retroactively registered as a foreign agent.