(CNN) Rudy Giuliani used a 2017 Oval Office meeting with President Donald Trump to press Rex Tillerson, then-secretary of state, to support a prisoner swap to resolve the Justice Department's prosecution of a Turkish businessman accused of violating Iran sanctions, a person briefed on the meeting tells CNN.

The businessman, Reza Zarrab, had ties to top Turkish government officials, who had pushed the US to drop charges that Zarrab had violated US sanctions on Iran's nuclear program. He was a client of Giuliani's.

During the White House meeting, the President invited Giuliani and Michael Mukasey, the former attorney general, to make their pitch to Tillerson, the source says.

After the meeting Tillerson mentioned the discussion to then-chief of staff John Kelly, who was not in the meeting, noting that it was a deal he could not support.

The episode is another reflection of Trump attempting to use his office to influence ongoing Justice Department proceedings. And news of it comes as his relationships to both Giuliani and Turkish President Recep Tayyip Erdoğan come under scrutiny.

Giuliani suggested the swap of Zarrab for an American pastor held by Turkey, Andrew Brunson. Asked by the President whether the deal was one he could support, Tillerson said he couldn't intervene, citing the ongoing Justice Department court case.

The President asked Tillerson if the deal was something Jeff Sessions, then the attorney general, could do. Tillerson responded that Sessions would have to contend with the fact it was an ongoing case headed for trial. He also told the President that it would be bad policy because it could put other Americans in danger, raising the prospect more hostages could be used as leverage for similar deals.

Mukasey, who was working alongside Giuliani to represent Zarrab, told the President it was an arrangement he could order as president, since it was within his power. Trump told Tillerson and Giuliani to see if they could work out an arrangement.

Tillerson said after he could not support it.

Giuliani pursued the possible deal directly with Tillerson after the Oval Office meeting and was rebuffed, the source said. Giuliani and Mukasey also made a similar pitch to Justice Department officials, who objected, according to sources briefed on those discussions.

Mukasey, reached Thursday, said he wouldn't discuss the White House meeting and declined comment. The White House did not respond to a request for comment. Tillerson did not immediately respond to a request for comment.

Giuliani initially denied the episode to Bloomberg, but later, he told the outlet it was possible that it was true.

"Suppose I did talk to Trump about it -- so what? I was a private lawyer at the time," Giuliani told Bloomberg. "Maybe I'm wrong. Maybe at some point I dropped his name in a conversation. Or maybe one of his people talked to him about it because I was trying to do a prisoner swap."

The revelation comes as Democrats probe Trump's ties with Giuliani, who played a central role in efforts to secure dirt on Joe Biden from Ukraine. Trump's own phone call with Ukraine's President asking him to investigate Biden is central to ongoing impeachment efforts.

Meanwhile, Trump's relationship to Erodgan has gained renewed attention after he spoke with the authoritarian leader over the weekend and abruptly announced that US troops would withdraw from northern Syria, clearing the way for a Turkish incursion.

Since leaving the State Department in 2018, Tillerson has spoken out about Trump's habit of asking him to do things unaware that such actions would violate the law.

"When the President would say, 'Here's what I want to do and here's how I want to do it.' And I'd have to say to him, 'Well Mr. President, I understand what you want to do, but you can't do it that way. It violates the law,' " he said during a fundraiser in December.

Tillerson said Trump would get "really frustrated" when told his requests would be illegal.