Ms Daniels sued to undo a non-disclosure agreement she signed in 2016 that she said was meant to silence her about a sexual encounter she had with Mr Trump a decade earlier.
She has alleged that she had sex once in 2006 with Trump and was paid shortly before the 2016 election to keep quiet about it. Daniels claims Cohen's denials portray her as a liar and sued for defamation.
"Any guy, in my experience, who has to constantly tell you how tough he is.is not a tough guy", Avenatti said of Michael Cohen, the attorney who was the subject of Federal Bureau of Investigation raids on Monday. The case appeared to be headed towards arguments about whether it should be arbitrated, but thanks to a stunning Federal Bureau of Investigation raid on Cohen's office and residence earlier this week, the lawsuit is now taking an abrupt turn.
Avenatti told Wallace that he and Clifford would oppose the stay, noting that Cohen "knows where a lot of bodies are buried".
The FBI agents who raided Cohen's office were looking for information on potential campaign finance violactions, The New York Times reported on Wednesday.
Daniels has until Monday evening to file her opposition, and then Cohen will have through Tuesday evening to respond to her.
But on Thursday, Avenatti said he learned Cohen won't be answering any questions at all and that Cohen will be seeking an emergency stay against the defamation suit.
Trump made his first public remarks about the case on April 5, telling reporters aboard Air Force One he had no prior knowledge of the payment.
The judge recently admonished the parties to meet and confer with each other before making filings in the case - and that apparently happened here as Michael Avenatti, plaintiff's attorney, first leaked what would happen in an appearance this afternoon on MSNBC.
Trump has been outspoken in the past about the character of people who invoke their Fifth Amendment rights. "And I'm going to paraphrase some of those quotes, he said only mobsters plead the Fifth and you only plead the Fifth if you're guilty".
Avenatti has asked Otero that a hearing on the renewed motion to depose be scheduled for May 7.