Cohen completed a third day of testimony on Capitol Hill Thursday, one day after publicly branding his former boss a racist and a con man who lied about business dealings in Russian Federation and directed him to hide extramarital relationships.
Like its House counterpart, this committee also oversees USA intelligence agencies.
Multiple Democrat-led House committees are pledging to investigate not only Mr Trump's campaign's ties to Russian Federation, which are also the subject of special counsel Robert Mueller's probe, but presidential conflicts of interest, possible money laundering and other oversight matters that Democrats said were ignored under GOP control. In reality, it was reported early past year that Cohen was shopping a book called Trump Revolution: From The Tower to The White House, Understanding Donald J. Trump.
The chief financial officer of Trump's business empire, Weisselberg began working for the company as an accountant for Trump's late father, Fred. The president denies the affair.
"And on the 26th floor", replied who Cohen, who when asked why that particular floor is important responded, "It was Mr. Trump's floor".
The committee's chairman Elijah Cummings indicated the panel could bring in a broad swathe of people that Mr Cohen mentioned. Daniels was also mentioned frequently.
In his Friday tweets, Trump highlighted Davis's associations with the 2016 Democratic presidential nominee, Hillary Clinton, whom he referred to as "Crooked Hillary".
But that false narrative was exposed on August 21, when Cohen pleaded guilty to campaign finance violations for arranging - "in coordination and at the direction of" Trump - payments of $130,000 to Daniels and $150,000 to Playboy model Karen McDougal. At a hearing in April, Cohen's attorney said that Hannity was another of Cohen's clients.
He said prosecutors in NY were investigating conversations Mr Trump or his advisers had with him after his office and hotel room were raided by the Federal Bureau of Investigation last April. Cohen said he could not discuss that conversation, the last contact he said he has had with the president or anyone acting on his behalf, because it remains under investigation. Jim Jordan of OH and Mark Meadows of North Carolina, sent a referral to the Justice Department alleging Cohen lied in his testimony.
In response to questioning from another lawmaker, Cohen said that he had seen Trump's tax returns, but had not gone through them.
They pointed to Cohen's guilty plea for making false statements to a banking institution and to court filings that say Cohen told friends he wanted a White House job.
Whether Democrats ultimately call Hannity into testify is far from clear.
During the interview, Cohen is pressed by CNN's Chris Cuomo about whether he would move from NY to Washington with Trump.
On Thursday, Hannity said on Fox News that Cohen told him that he made decision to pay Daniels and did not tell Trump.
"This has obviously been an excruciating time for him", Schiff said.