Chaffetz's reported early departure comes after he took to Twitter on Wednesday to announce that the House Oversight Committee "officially scheduled" a hearing with former FBI Director James Comey - though he hasn't heard back yet.
Jason Chaffetz, R-Utah, tweeted that he's asked Comey to testify at the hearing.
On Tuesday, shortly after the existence of memos by Mr. Comey was reported, Mr. Chaffetz sent a letter to Andrew McCabe, the acting director of the Federal Bureau of Investigation, asking for all documents relating to communication between Mr. Trump and Mr. Comey.
A separate letter, addressed to acting FBI Director Andrew McCabe, sought notes or memos written by Comey about conversations he had with senior White House and Department of Justice officials related to the Russian Federation investigation.
The letters come on the heels of a New York Times report that Comey had written a memo detailing a conversation with the president in which Trump allegedly asked him to stop the inquiry into National Security Adviser Michael Flynn.
In a conference call with Iowa reporters on Wednesday, Grassley said he plans to exercise the committee's oversight responsibilities.
Comey declined to testify before the Senate Intelligence Committee in the days following his firing.
Chaffetz, R-Utah, said Wednesday afternoon that he had yet to issue the invitation because Comey "evidently has a new (number)".
"What I have been doing is trying to give the chairman space to heal and then we have to figure out what to do", Cummings said. Members of the Senate Judiciary Committee also planned to ask Comey to testify, The Hill reported. "I hope you can let this go".
Chaffetz, in his role as committee chairman, on Tuesday requested any "memoranda, notes, summaries and records referring or relating to any communications between Comey and the president".
It is most likely that Comey will testify before Congress about his meetings and interactions with Trump and also on the Moscow's meddling in U.S. Presidential election and the links of Trump campaign officials with Russian officials.
President Trump fired Comey last week following which the administration officials provided multiple, conflicting accounts of the reasoning behind the dismissal.