In response to a request for comment on Graham's announcement, Giuliani told CNN, "Love Lindsey, but I am still a lawyer and I will have to deal with privilege".
Graham said on Twitter that he would extend the invite after hearing "disturbing allegations" about corruption in Ukraine and "the many improprieties surrounding the firing of former Prosecutor General Viktor Shokin".
The House Democrats and an unidentified whistleblower have accused Trump using his office to pressure Ukraine to investigate Joe Biden and his son, Hunter, regarding their dealings in the Eastern European country.
"Given the House of Representatives' behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine", Graham, R-S.C., said in his tweet.
Senate Judiciary Committee Chairman Lindsay Graham, a fellow Republican, said on Tuesday he would invite Giuliani to testify before his committee.
Democratic Sen. Dianne Feinstein, the committee's ranking member, said she, too, would like to hear from Giuliani. Cory Booker of New Jersey, Kamala Harris of California and Amy Klobuchar of Minnesota.
"I don't want to turn the Senate into a circus", Graham added.
Text messages between top USA diplomats that were released by the House Intelligence Committee have corroborated the whistleblower's claim that Giuliani was involved in Trump's push to have Ukrainian President Volodymyr Zelensky investigate the Bidens. Accusations of wrongdoing by the Bidens have not been substantiated, leading Democrats to say Giuliani has been pushing conspiracy theories.
Giuliani told the Washington Post that he was "very interested" in speaking to the Senate committee, but that "there are a lot of legal issues to consider" first. It's unclear if he'll derive the invitation, as the Trump Administration has blocked a mode of witnesses from testifying sooner than the Dwelling.
The chairmen of the three House committees that have subpoenaed Giuliani have given him until October 15 to respond to them, but he says he's ready to challenge them on the summons.
Giuliani is at the center of the storm over Trump's attempt to pry damaging information about Biden out of Ukraine.
Trump and Giuliani also have suggested that Ukraine was involved in interfering in the 2016 election as they've sought to undermine the origins of Special Counsel Robert Mueller's probe into Russian election meddling, an allegation Ukrainian officials have rejected.
Giuliani has stated that he shared all of the details of his conversations with Yermak with the State Department.
-With assistance from Jordan Fabian.