As a representative of his consulting firm, Flynn Intel Group, Flynn met with senior representatives of President Recep Tayyip Erdogan's government in September 2016, Woolsey said. Woolsey was a Trump campaign adviser at the time and attended the meeting, but said he arrived after it was already well underway.
Woolsey claims that those present discussed sending Fethullah Gulen, a Muslim leader who Erdogan has accused of being behind a failed military coup to overthrow him, back to Turkey to face charges -- possibly outside the legal US extradition system.
"What I saw and heard was sort of the end of the conversation -- it's not entirely clear what transpired because of that," Woolsey said on "CNN Tonight" with Don Lemon. "But it looks as if 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, the rival for Turkey's political situation."
A spokesman for Flynn flatly denied Woolsey's characterization of the meeting.
"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 New York is false," Flynn spokesman Price Floyd said in a statement. "No such discussion occurred. Nor did Mr. Woolsey ever inform General Flynn that he had any concerns whatsoever regarding the meeting, either before he chose to attend, or afterwards."
The Wall Street Journal first reported
Woolsey's claims Friday.
Flynn was advising the Trump campaign at the time. He became national security adviser after Donald Trump became President in January but resigned in mid-February
, after he reportedly misled administration officials about his communications with the Russian ambassador to the United States.
Woolsey, who was CIA director under President Bill Clinton and was on President Trump's team for about five months before quitting
in January, said he didn't hear enough of what was said to make any definitive statements about what happened before he got there.
"The reason I'm being cautious about how this was worded is because I wasn't there for much of this meeting," said Woolsey, who nevertheless described the meeting as "suspicious" and "concerning."
"I felt I needed to say something to somebody, but was it a clear plot that they were going to seize him? No," he said.
The White House acknowledged
earlier this month that Trump's transition team was aware Flynn engaged in work that would likely require him to register his consulting firm as a foreign agent before he was tapped to serve as national security adviser.
Flynn Intel Group received $530,000 in payments from a Turkish-owned company based in the Netherlands and earlier this month registered as a foreign agent with the Justice Department, acknowledging that the work may have benefited the Turkish government, according to foreign agent registration paperwork filed with the department.
Flynn's firm was not compensated by the Turkish government, but by Inovo BV, a company owned by Turkish businessman Ekim Alptekin, according to the Justice Department filing. Alptekin is also the chairman of a US-Turkish business council.
However, as part of that work, Flynn met with Turkish government officials in September 2016, including Turkey's ministers of foreign affairs and energy, his firm disclosed in the filing. The meetings came around the time when Flynn traveled regularly with Trump on his private plane and frequently introduced him at campaign rallies.