Giuliani was probing discredited allegations that Biden, when he was vice president, sought the firing of Ukraine's chief prosecutor to halt the investigation of a gas company on which his son, Hunter Biden, was a board member.
Parnas, who was born in Ukraine, and Fruman, in Belarus, are both USA citizens now.
The WSJ report cites information from a Soros-funded group, the Organized Crime and Corruption Reporting Project (OCCRP), alleging that the men had dinner with the president in May 2018 and later that month met with Donald Trump Jr.
Ms Yovanovitch was the third key witness to appear in the impeachment inquiry.
"That sent a shiver through the whole Foreign Service, which was already shivering about how Trump was treating them and Pompeo wasn't defending them", the person said.
Prosecutors allege businessmen used wire transfers from a corporate entity they controlled to make the donation in 2018.
The investigation of Mr Trump could lead to the approval of articles of impeachment - or formal charges - against the president in the House.
The next hearing in the Parnas and Fruman case is scheduled for 17 October at 3:00 p.m. [7:00 p.m. GMT] at the US District Court for the Southern District of NY.
On May 9, 2018, Parnas posted a photo of himself and his business partner David Correia with Sessions in his Capitol Hill office, with the caption "Hard at work!" Giuliani declined to comment on the reasons for their travels.
Two men linked to Trump's lawyer Giuliani arrested on campaign-finance violations
Giuliani is a key figure in House Democrats' investigation for his coordination of meetings with Ukrainian officials for Trump. They four also accused of also taking steps to evade contribution limits on political donations by using straw donors.
According to the indictment, the men also played a role in another incident House Democrats are zeroing in on: Parnas allegedly pressed an unidentified congressman to push for the ouster of the USA ambassador to Ukraine at the behest of Ukrainian government officials. Prosecutors told the court they were a flight risk; a judge ordered them held on $1 million bail. They sought to influence politicians on behalf of the Ukrainian government, according to the indictment. Kukushkin has been arrested in California, but Correia remains at large, the official said. The investigation remains ongoing.
Prosecutors say the two men shielded the foreign source of the funds by laundering through their US business.
The commitment to raise more than $20,000 for the congressman was made in May and June 2018.
According to federal campaign finance law, an independent expenditure - such as 35th Inc. - involves election spending "that is not made in cooperation, consultation, or concert with, or at the request or suggestion of, a candidate, a candidate's authorized committee, or their agents, or a political party committee or its agents". In a statement, Sessions said he "could not have had" knowledge of the alleged scheme.
Parnas appears to have further financial connections to Trump.
An unnamed foreigner wired $500,000 from a bank account overseas through NY to the defendants for contributions to two candidates for state office in Nevada, the indictment alleges.
The indictment accuses the four men of also participating in a scheme to acquire retail marijuana licenses through donations to local and federal politicians in New York, Nevada and other states. Parnas says that he has known Giuliani for years.
"We take our legal obligations seriously and scrupulously comply with the law and any suggestion otherwise is false", the statement said.
Neither Giuliani nor the effort to discredit Biden are mentioned in the indictment, but it does give details of a political donation to an unnamed congressman in 2018, whose help they sought in seeking to oust the then U.S. ambassador to Kyiv, Marie Yovanovitch, who was putting pressure on the Ukrainian government at the time to tackle corruption. The Washington Post obtained new details about the extent of the lobbying effort to kill the case - including the presence of Zarrab's attorneys in the Oval Office and a visit Giuliani made to the Justice Department around the same time to ask for the case to be dropped. That conversation is now at the heart of the impeachment inquiry.
The House committees overseeing the impeachment inquiry issued subpoenas for Mr. Parnas and Mr. Furman to testify and turn over documents. He was reportedly also at meetings in late January in NY and mid-February in Warsaw with Giuliani and Yuriy Lutensko, another former prosecutor general for Ukraine.
Parnas has told NPR that he worked as a fixer to help arrange meetings for Giuliani with current and former Ukrainian officials, including prosecutors.