Bondy tells CNN that his client and Nunes began communicating around the time of the Vienna trip. Parnas says he worked to put Nunes in touch with Ukrainians who could help Nunes dig up dirt on Biden and Democrats in Ukraine, according to Bondy.
That information would likely be of great interest to House Democrats given its overlap with the current impeachment inquiry into President Trump, and could put Nunes in a difficult spot.
Bondy tells CNN his client is willing to comply with a Congressional subpoena for documents and testimony as part of the impeachment inquiry in a manner that would allow him to protect his Fifth Amendment rights against self-incrimination.
Parnas' claims that Nunes met with Shokin, which has not been previously reported, add further context to a Daily Beast report
that Parnas helped arrange meetings and calls in Europe for Nunes last year, citing another Parnas' lawyer, Ed McMahon.
Those revelations came to a head on Thursday when Democratic Rep. Eric Swalwell raised the Daily Beast story publicly during the impeachment hearing.
Parnas, who was indicted on federal campaign finance charges last month, worked with Shokin and Giuliani to push a pair of unfounded claims: that Ukrainians interfered in the 2016 election on behalf of Democrats, and that Biden was acting corruptly in Ukraine on behalf of his son Hunter, who sat on the board of Ukrainian gas company Burisma Holdings.
According to Bondy, Parnas claims Nunes worked to push similar allegations of Democratic corruption.
"Nunes had told Shokin of the urgent need to launch investigations into Burisma, Joe and Hunter Biden, and any purported Ukrainian interference in the 2016 election," Bondy told CNN.
There is no evidence that the Bidens acted inappropriately. Nor is there evidence to support the conspiracy theory that Ukraine worked with Democrats to interfere in the 2016 election.
Yet these claims have been a key part of the public defense of the President put forth by Nunes and other Republicans during the impeachment hearings this month.
Parnas is currently under house arrest in Florida and has pleaded not guilty to charges of federal campaign finance fraud.
Over the past two weeks, CNN approached Nunes on two occasions and reached out to his communications staff to get comment for this story.
In the Capitol on Nov. 14, as CNN began to ask a question about the trip to Vienna, Nunes interjected and said, "I don't talk to you in this lifetime or the next lifetime."
"At any time," Nunes added. "On any question."
Asked again on Thursday about his travel to Vienna and his interactions with Shokin and Parnas, Nunes gave a similar response.