Former Trump adviser George Papadopoulos told Fox News' Maria Bartiromo in an exclusive interview that he is heading back to Greece to retrieve $10,000 that he suspects was dropped in his lap as part of an entrapment scheme by the CIA or FBI -- and federal investigators want to see the marked bills, which he said are now stored in a safe.

Papadopoulos said on "Sunday Morning Futures" he was "very happy" to see Devin Nunes, R-Calif., grill former Special Counsel Robert Mueller about the summer 2017 payment during last week's hearings -- even though Mueller maintained, without explanation, that the matter was outside the scope of his investigation.

"I was very happy to see that Devin Nunes brought that up," Papadopoulos said. "A man named Charles Tawil gave me this money [in Israel] under very suspicious circumstances. A simple Google search about this individual will reveal he was a CIA or State Department asset in South Africa during the '90s and 2000s. I think around the time when Bob Mueller was the director of the FBI.

"So, I have my theory of what that was all about," Papadopoulos added. "The money, I gave it to my attorney in Greece because I felt it was given to me under very suspicious circumstances. And upon coming back to the United States I had about seven or eight FBI agents rummaging through my luggage looking for money."

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According to Papadopoulos, "the whole setup" by the "FBI likely, or even the special counsel's office," was intended to "bring a FARA [Foreign Agents Registration Act] violation against me." The FARA statute played a key role in the prosecutions of former Trump aides, including Michael Flynn and Paul Manafort.

Papadopoulos previously told Bartiromo in May that he wanted authorities to take a look at the money trail.

"I actually want Congress, [Bill] Barr, [DOJ Inspector General Michael] Horowitz, and [U.S. Attorney John] Huber to review the bills because I still have the bills and I think they are marked," Papadopoulos said. "These bills that are still in Athens right now must be examined by the investigators because I think they are marked and they're going to go all the way back to DOJ, under the previous FBI under [James] Comey, and even the Mueller team."

He added: "If the Mueller team is going around entrapping campaign associates and Trump associates, the way they did to me — I am sure it wasn't just me they did it to — it's going to open up a massive can of worms," Papadopoulos said. "I think we need to get to the bottom of exactly not only how did this story start, but why were they entrapping us moving forward."

Recounting the alleged 2017 episode, Papadopoulos said, "I was reached out to once again by another person who wanted to do business with me. And I was on vacation with my then girlfriend now wife, in Greece, and he comes to me he says why don't you come to Israel with me and let's talk about working together. I go to Israel with him, and he drops $10,000 in my lap in a room, in Tel Aviv. I don't understand what is happening, I am very disturbed by the events. I fly to Athens the next day and give the money to my lawyers and this person tells me he doesn't want his money back, so immediately I thought there was something wrong."

In a court filing last year, Mueller's prosecutors wrote that Papadopoulos “provided information about $10,000 in cash he received from a foreign national whom he believed was likely an intelligence officer of a foreign country (other than Russia)."

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“The defendant has stated that he kept that money in a safe pending his sentencing in this case and Counsel for the defendant has consented to the imposition of this fine amount,” Mueller's team wrote. (Mueller's halting and weary performance in last week's hearing has left commentators and lawmakers questioning how much involvement Mueller had in drafting his 448-page report, as well as various court filings throughout the probe.)

Papadopoulos pleaded guilty in 2017 to lying to federal investigators, and Mueller recommended he serve prison time in the filing. The former Trump aide ultimately served 12 days in prison and paid a $9,500 fine.

Meanwhile, the Justice Department’s internal review of the Russia investigation is zeroing in on transcripts of recordings made by at least one government source who met with Papadopoulos overseas in 2016, specifically looking at why certain "exculpatory" material from them was not presented in subsequent applications for surveillance warrants, according to two sources familiar with the review.

The sources also said the review is taking a closer look at the actual start date of the original FBI investigation into potential collusion between members of the Trump campaign and the Russians, as some allege the probe began earlier than thought. Both components are considered key in the review currently being led by Barr and U.S. Attorney from Connecticut John Durham -- an effort sure to draw more attention in the coming weeks and months now that Mueller's testimony is over.

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The recordings in question pertain to conversations between government sources and Papadopoulos, which were memorialized in transcripts. One source told Fox News that Barr and Durham are reviewing why the material was left out of applications to surveil another former Trump campaign aide, Carter Page.

“I think it’s the smoking gun,” the source said.

“These recordings have exculpatory evidence,” the other source added. “It is standard tradecraft to record conversations with someone like Papadopoulos — especially when they are overseas and there are no restrictions.”

Prior to the 2016 presidential election, Papadopoulos met with Maltese professor Joseph Mifsud in London, who told him that the Russians had dirt in the form of emails that could damage Hillary Clinton’s presidential campaign. Papadopoulos then told Australian diplomat Alexander Downer of the new information. Downer reported Papadopoulos’ comments to him to the FBI.

A source told Fox News that the "exculpatory evidence" included in the transcripts is Papadopoulos denying having any contact with the Russians to obtain the supposed "dirt" on Clinton.

On Sunday, Papadopoulos told "Sunday Morning Futures" that "about the moment I joined the Trump campaign, I'm being invited by the former foreign minister of Italy to meet Joseph Mifsud, after I was introduced to this foreign minister by a company I used to work for, which is connected to the MI6. So clearly, there was some sort of global or at least European radar on me while I was living in London and as soon as I was joining the Trump campaign -- which not even the media knew at the time -- I'm being introduced to Joseph Mifsud, in Rome, at a school that trains the CIA and the FBI."

He added: "So, why I was introduced to Joseph Mifsud, and why this company introduced me to Joseph Mifsud, now that we know they're connected to MI6 and the FBI, makes things even more suspicious and a lot more damning, in my opinion."

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Papadopoulos did not only meet with Mifsud and Downer while overseas. He met with Cambridge professor and longtime FBI informant Stefan Halper and his female associate, who went under the alias Azra Turk. Papadopoulos told Fox News that he saw Turk three times in London: once over drinks, once over dinner and once with Halper. He also told Fox News back in May that he always suspected he was being recorded. Further, he tweeted during the Mueller testimony about "recordings" of his meeting with Downer.

It is unclear, at this point, which of these individuals may have recorded conversations with Papadopoulos. Mifsud was conspicuously not charged in Mueller's probe -- a point Ohio Rep. Jim Jordan, a Republican, hammered repeatedly during last week's hearings.

Former Rep. Trey Gowdy, R-S.C., now a Fox News contributor, first signaled the existence of transcripts of secretly recorded conversations between FBI informants and Papadopoulos earlier this year.

“If the bureau’s going to send in an informant, the informant’s going to be wired, and if the bureau is monitoring telephone calls, there’s going to be a transcript of that,” Gowdy said in May on Fox News' “Sunday Morning Futures,” acknowledging he was aware of the files and suggesting they included exculpatory information.

Fox News' Brooke Singman and Maria Bartiromo contributed to this report.