Government officials might have obtained a key witness to aid in their investigation of Russian meddling in the 2016 presidential elections.
Cohen demanded the satirical news organization remove the article immediately and issue an apology.
The president's former personal attorney previously stated that a deal for a Trump Tower in Moscow was dead in January 2016.
The forms were referred to the Justice Department following a complaint by the watchdog group Citizens for Responsibility and Ethics in Washington (CREW).
"Ms. Daniels's case has never been stronger," Michael Avenatti told Newsweek.
"So if I were you, I would tell Mr. Trump to find someone else to fabricate things about me," Avenatti wrote in an email.
Trump reportedly uses Hannity "to decompress" at night.
Avenatti's critics often point to his media appearances in an attempt to discredit him.
Rudy Giuliani claimed that he would use his law firm's funds to make payments similar to the one made by Michael Cohen to Stormy Daniels.
Michael Avenatti was responding to suggestions that he was a campaign operative.
Payments by large corporations to Cohen's Essential Consultants has raised awkward questions for the president.
Former Novartis CEO Joseph Jimenez joined the leadership of lobbying heavyweight PhRMA just before his company agreed to pay more than $1 million to Michael Cohen's shell company.
"You've got millions of dollars that are being deposited into this account," Avenatti said.
"Who knew Mr. Cohen was such a brilliant renaissance man?" Michael Avenatti tweeted.
The lawyer for Stormy Daniels has claimed that $500,000 was deposited into the same account Michael Cohen used to silence Stormy Daniels.
The president's longtime personal attorney was subject to a raid by federal authorities last month.
Melania Trump's 57 percent favorable rating is greater than any rating her husband has received since CNN began polling around him in 1999.
Daniels made a surprise appearance on 'Saturday Night Live' last night.
Trump previously said Bannon "has nothing to do with me or my presidency," and, "when he was fired, he not only lost his job, he lost his mind."