A pair of GOP chairmen are floating the idea of investigating former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE as Democratic calls grow for President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE to be impeached over his communications with Ukraine's leader.

Sens. Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' The Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination MORE (R-Wis.) and Lindsey Graham Lindsey Olin GrahamLincoln Project mocks Lindsey Graham's fundraising lag with Sarah McLachlan-themed video The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election Trump dumbfounds GOP with latest unforced error MORE (R-S.C.) both raised the possibility of an investigation into Biden after the White House released a record of a July 25 phone call that showed Trump asking Ukrainian President Volodymyr Zelensky to look into Biden.

Democrats have reacted to the records released by the White House by saying they make the case for impeachment, but Republicans are countering with calls for Biden to be investigated.

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"I've got some real legitimate questions about what happened with Vice President Biden, Hunter Biden, what was happening over there. ... I have a lot of questions that should be answered," Johnson, chairman of the Senate Homeland Security and Governmental Affairs Committee, told reporters on Wednesday.

He said that it would be "completely appropriate" for the Senate to probe Biden.

Asked if there would be a Senate investigation, he added: "As part of my oversight responsibilities we continue to ask questions, we continue to gather information, oversight letters on a host of issues, that would certainly be one of them."

Trump and his allies have latched onto Biden’s connection to Ukraine as the former vice president seeks the Democratic nomination to challenge Trump in 2020.

Hunter Biden worked on the board of a natural gas company owned by a Ukrainian oligarch while his father served as vice president. Joe Biden pushed in 2016 for the dismissal of a Ukrainian prosecutor who had been accused of overlooking corruption in his own office, threatening to withhold money if the prosecutor was not fired.

There’s no indication Joe Biden was acting with his son’s interests in mind and the former vice president has denied doing so. But Trump and his allies, including Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE, have pushed for an investigation into the Bidens in Ukraine and decried the former vice president as “corrupt.”

Trump, according to a five-page readout of the call, suggested Zelensky work with Giuliani to investigate, telling him "whatever you can do with the attorney general would be great."

Graham, who chairs the Senate Judiciary Committee, said on Wednesday that he thought someone "should look at corruption," but that the probe should be outside of the Senate.

"I hope somebody will look at why the guy was fired," he added.

Graham, a close ally of Trump's on Capitol Hill, has called for a probe into the Bidens amid reports that Trump and Giuliani urged Ukraine to investigate Biden.

He told radio host Hugh Hewitt that he thought without an investigation there would be a double standard against Trump, who was at the center of a two-year investigation into the 2016 election.

"The prosecutor was looking at things in the Ukraine, and he got fired, and there’s all kind of allegations about the Ukraine dumping information into the legal system and political system in 2016 about [Paul] Manafort and others, you know, Hunter Biden, what kind of situation did he have financially?" Graham asked.

Morgan Chalfant contributed