In this 2017 photo, former New York City Mayor Rudy Giuliani is seen at Trump Tower in New York City.
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(CNN) —  

The top Senate Democrat said Thursday President Donald Trump’s personal lawyer, Rudy Giuliani, needs to testify before Congress after two of his associates – who helped dig up dirt in Ukraine on Democratic presidential candidate Joe Biden – were arrested and charged with trying to funnel foreign money into US elections.

“There are now new reports, very troubling, that two Giuliani associates are being indicted on criminal charges by the Southern District,” said Senate Minority Leader Chuck Schumer, a Democrat from New York said at a Manhattan news conference

“Giuliani has been involved up to his neck in this entire mess,” the senator said. “He has an obligation to testify under oath so he can be asked questions so this can come to light.”

Senate Judiciary Committee Chairman Lindsey Graham, a Republican from South Carolina, said this week he wants to convene hearings to examine allegations of corruption in Ukraine.

“Given the House of Representatives’ behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine,” said Graham in a tweet. “Therefore I will offer to Mr. Giuliani the opportunity to come before the Senate Judiciary Committee to inform the committee of his concerns.”

The former New York City mayor told CNN’s Michael Warren that since he’s the President’s lawyer, he might have to make sure executive privilege wouldn’t prevent him from testifying: “Love Lindsey but I am still a lawyer and I will have to deal with privilege.”

But he later suggested he might appear, although nothing is set up yet.

“Given the nature of his invitation about my concerns I might be able to do it without discussing privileged information,” he said.

It’s unclear if the arrests of his associates will impact Giuliani’s desire to testify.

The two associates of Giuliani – Igor Fruman and Lev Parnas – appeared in court Thursday in Virginia, where prosecutors told a judge they were concerned the two might attempt to flee. They haven’t entered a plea.

CNN’s Michael Warren contributed to this report.