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's personal lawyer 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 said he will make a decision soon about whether to accept Sen. 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's (R-S.C.) invitation to testify before Congress about Ukraine.

“That’s a decision I’ve got to make with my client over the course of the next week or so,” Giuliani told Hill.TV on Wednesday without elaborating further.

His comment came a day after Graham changed course, and announced plans to invite the former New York City mayor to testify before before the Senate Judiciary Committee.

The senator previously indicated that he wanted "all things Ukraine" investigated but didn't think the Senate should lead the probe.

“Given the House of Representatives’ behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine,” Graham said in a series of tweets.

While Graham didn’t specifically mention 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, he added that he made the decision after hearing “numerous occasions disturbing allegations” from Giuliani about alleged corruption in Ukraine, particularly concerning the firing of the country's then-top prosecutor general Viktor Shokin.

The announcement comes as Trump and his allies double down over claims that Biden, while serving as vice president, pushed for Shokin to be fired in order to help his son, who serves on the board of a Ukrainian energy company.

There has been no evidence of wrongdoing by the former Vice President.

Giuliani, meanwhile, has become a key figure in the ongoing House impeachment inquiry arising from Trump’s efforts to pressure Ukraine to investigate the Bidens.

House Democrats subpoenaed Giuliani last month as part of the investigation, though Giuliani denied this in his interview with Hill.TV.

“With regard to the House…I didn’t get a subpoena — I’ve gotten a letter,” he said. “They haven’t gotten to the stage of a subpoena.”

—Tess Bonn