"I know for a fact that this is not the only tape," Avenatti said after it emerged that Cohen had recorded Trump discussing a payment to an ex-Playboy model.
The performer was arrested last week but charges were dropped.
Michael Avenatti said he would consider running against Donald Trump in 2020 because America can't afford to "relive 2016."
Avenatti said he ultimately believes Cohen will “flip” on the president if prosecutors offer him a deal in return for cooperation.
“The government does not appear to have the ability or the will to make it happen," Avenatti told Newsweek. "We’re going to see if we can make it happen.”
“Imagine our adversaries in the world as they learned how easy it was for a comedian to bypass security measures and reach the president. They are rolling."
Avenatti denied having a personal interest in the pot farm.
"These children need to be reunited with their parents and it needs to happen now," Avenatti said.
Avenatti said a possible gag order should go “both ways by extending to all parties,” including Trump and Giuliani, who have both been vocal about the case on TV and Twitter.
Prosecutors were to meet with Daniels to discuss their investigation into Trump's former fixer Michael Cohen.
“I am headed down in a week. Don't worry,” she tweeted in response to someone asking her to help the migrant kids.
Michael Avenatti, the lawyer representing Stormy Daniels in her case against President Donald Trump, is wading into the immigration battle.
“What’s going to happen here is the narcissism of this president, his arrogance, his stupidity, is ultimately going to catch up to him," Avenatti said of Trump.
Michael Avenatti has frequently attacked President Donald Trump's personal lawyer, Rudy Giuliani.
“If we weren’t a threat, none of this would be happening,” Avenatti said.
“Absolutely, I have a lot of sympathy for the first lady,” Avenatti said.
Is this is a preview of a possible show?
“If any atty for any Fortune 500 co. made the public comments that Giuliani did yesterday (which he affirmed this morning), they would be immediately fired," Avenatti tweeted.
"There are numerous expenses associated with cases like this and here, security costs alone are astronomical," Avenatti tweeted.
Avenatti’s claim came the same day a report alleged he personally contacted top Democratic operatives for financial help in his legal fight against Trump.
Avenatti also said he would be demanding access to any audiotapes featuring Stormy Daniels's former lawyer and Cohen.