"They did no legal or lobbying work for us, and the contract ended in December 2017," AT&T said.
The company did not say how much it had paid Cohen, who was the president's personal lawyer at the time.
AT&T is in the midst of pursuing an $85 billion acquisition of Time Warner. The U.S. Justice Department has sued to block that deal.
In a report on Cohen's company, Avenatti's law firm said that Novartis in late 2017 and early 2018 made four separate payments to Essential Consultants totaling nearly $400,000.
"Following these payments, reports surfaced that Mr. Trump took a dinner with the incoming CEO of Novartis before Mr. Trump's speech at the World Economic Forum in Davos, Switzerland in late January 2018," Avenatti's report said.
That CEO, Vas Narasimhan, was joined with a group of other companies' executives at that dinner.
A Novartis spokesperson said in a statement that "any agreements with Essential Consultants were entered before our current CEO taking office in February of this year and have expired."
The White House declined to comment on whether Trump knew about payments to Cohen from AT&T, Novartis or Columbus Nova, the company linked to the Russian oligarch, and instead referred questions to the president's outside legal team.
Avenatti's report says another company, Korea Aerospace Industries LTD, paid Essential Consultants $150,000 in November 2017.
Avenatti's client Daniels, whose real name is Stephanie Clifford, was paid $130,000 by Essential Consultants on the eve of the 2016 presidential election.
Daniels says the money was in exchange for her signing a deal that required her to remain silent about an affair she claims to have had with Trump in 2006, shortly after the birth of his youngest son.
The White House has denied that Trump had sex with the adult film actress.
Cohen did not have an immediate comment on Avenatti's new allegations about payments to Cohen's company.
CNBC's Eamon Javers contributed to this report.