But on Monday, the White House press secretary issued a statement saying, "The president's power to assert executive privilege is well-established".
Senior United States Senator Richard Burr, who has spoken to Comey several times expects the former Federal Bureau of Investigation director to talk in detail about his conversations with Trump when he testifies openly before the committee.
Those struggles are coming to a head as fired FBI Director James Comey is set to testify on Capitol Hill Thursday.
Comey's testimony will be the first public remarks since he was summarily fired by Trump in early May, and represent a moment of great peril for this already embattled president. However, New York Times says that the privilege of the USA president is not absolute and that the Supreme Court could have stopped him in his tracks despite the conversation between the President and his staff being confidential.
Invoking executive privilege would theoretically allow Mr. Trump to block Comey's testimony.
Analysts had speculated that Trump might use executive privilege to stop Comey from testifying. On Sunday, Senator Roy Blunt, a Missouri Republican and a member of the intelligence committee, said the president would be "better served by getting all this information out".
"Sooner rather than later, let's find out what happened and bring this to a conclusion", Blunt said on "Fox News Sunday".
Short had been speaking about the president's legislative priorities, including passing health care reform and major tax cuts, when he was asked how much harder it was to move forward when issues like former FBI Director James Comey's planned testimony and the ongoing Russian Federation investigations are sucking up so much oxygen on Capitol Hill.
Burr also told CNN that former White House national security adviser Michael Flynn, a focus of the Russian Federation probe, had turned over some of the documents to the Senate intelligence committee in response to a subpoena they issued last month.
Flynn was sacked after less than a month because of revelations that he misled Vice President Mike Pence about his communications with Russia's ambassador to the United States.
Trump asked Comey to drop the Flynn investigation, said a person who was given a copy of a memo Comey wrote about the conversation.
Trump adviser Kellyanne Conway said on ABC's "Good Morning America" on Friday that Trump and his staff would be "watching with the rest of the world" to see what Comey has to say.