Trump, for his part, has acknowledged he had the Trump-Russia investigation on his mind when he pulled the trigger on Comey's firing, as he admitted to NBC's Lester Holt in a nationally televised interview mere days after doing so.
Calls and emails to Kasowitz's NY firm were not immediately returned on Wednesday.
If all goes as predicted, Comey will publicly stand by his memos, including those in which Trump seemingly tried to stand in the way of the investigation.
FBI Director James Comey may testify in an open Senate hearing as soon as next week, while on the House side of the Russian Federation investigation subpoenas were approved for several individuals including former National Security Advisor Mike Flynn.
Trump is still on the hunt for a new FBI director three weeks after he fired Comey and expressed hopes of naming a new leader for the bureau before his first overseas trip, which ended Saturday. Mueller's separate probe could conceivably look at the circumstances surrounding Comey's firing.
Congress is now out of session. It resumes next Tuesday.
No firm date has been set for the hearing, according to CNN.
A spokeswoman for the committee's chairman, Sen. Its work - already the subject of intense public scrutiny - has received even more attention since Trump fired Comey as director amid a probe into whether Trump's campaign coordinated with Russians to influence the 2016 presidential election. Comey declined to do so.
Lieberman is one of five names Trump reportedly considered to replace Comey who have eliminated themselves from taking the post.
But later in the day, the White House showed it was beginning to offload the Russian Federation crisis to Trump's longtime personal attorney, Marc Kasowitz. That appears less likely now that Mueller and Comey have discussed the limits of his testimony.
Days before Trump left for the Middle East, the Comey bombshell hit and when he returns, the testimony that all of America is waiting for is threatening to happen all too soon for the White House.
Also Wednesday, a Justice Department official confirmed that Mueller had named a top Justice Department official to his team. John Cornyn of Texas, former U.S. Attorney Michael Garcia and Alice Fisher, the former head of the department's criminal division.