According to two sources close to the president, Trump has privately branded Avenatti a wannabe bigshot and a "loser".
AT&T said this week it engaged with Essential Consultants previous year so Cohen could provide "insights into understanding the new administration" and added the company did not lobby for the telecommunications giant.
Giuliani is now back-tracking.
Giuliani was then forced to backtrack, telling CNN that Trump "didn't interfere" with the Justice Department's case.
Rudy Giuliani, who was hired by the White House to help defend the special counsel's probe against President Donald Trump, is yet again backtracking on comments unrelated to the Russian Federation investigation that go against previous White House statements.
The former New York City mayor's specific reference to the president denying the merger was in contrast to comments from November when the Department of Justice's Assistant Attorney General for the Antitrust Division Makan Delrahim told ABC News, "I have never been instructed by the White House on this or any other transaction under review by the antitrust division".
"I don't get involved with pimps", Giuliani told Business Insider.
Sanders reiterated the president's statement, that the Department of Justice made the choice to oppose the merger.
Rudy Giuliani, center, an attorney for U.S. President Donald Trump, leaves after speaking at the Iran Freedom Convention for Human Rights and democracy at the Grand Hyatt, Saturday, May 5, 2018, in Washington.
Cohen had reached out to AT&T even before Stephenson's huddle with the president, the person said. "He did drain the swamp". The president denied the merger. How do we meet his management team at least to get an idea of how they think about things?
"People should recognize that he [Quinn] came to recognize it was a misjudgment - witness the fact a year ago that he terminated the contract, got out of it as fast as he could, and that's a point that's not being written right now as people pile on", the person said.
AT&T noted in the fact sheet that Cohen was among "several consultants" the company hired as Trump was assuming the presidency.
"There doesn't seem to be any involvement with us", he said.
However, Giuliani said he believes Cohen does not deserve the criticism he is taking from some in the media and in political circles.
This story is part of a pattern of Giuliani missteps. The consulting fee went through a shell company Cohen also used to pay hush money to Daniels over her alleged affair with Trump. It would be one of the biggest media deals ever if approved. The outstanding question: Did politics and Trump influence the DOJ's decision?
Trump has personally railed against the Time Warner-AT&T deal, a stance that may well have more to do with his burning hatred of CNN than anything else. So when he took office, there were concerns within AT&T and Time Warner that he or his aides would try to block the deal.
Under AT&T's rules, Quinn had significant leeway to approve the Cohen contract because its $600,000 price tag did not trigger oversight from more senior executives, according to a person familiar with the matter who spoke on the condition of anonymity to discuss internal company practices.