Daniels was performing at a strip club when she allegedly violated a no-touch law.
"If you weren't given permission to have that conversation with Michael Cohen you may have to. answer to an ethics committee", Dershowitz told Avenatti, while both men were speaking on CNN's "Anderson Cooper 360".
The judge said the constitution is "neither a trick nor an illusion" and told Blakely that his request was 'serious business'.
"Like a small-town carnival magician who attempts to confuse the audience with smoke and mirrors, Avenatti attempts to somehow justify his conduct by pulling the first amendment out of his tiny bag of tricks while at the same time pointing his finger at others", Blakely wrote in requesting the order.
Michael Cohen's efforts to muzzle one of his chief antagonists will be before a federal judge in Los Angeles on Friday, as President Donald Trump's long-time fixer seeks a gag order against Michael Avenatti, the outspoken attorney for adult-film star, Stormy Daniels.
Asked if he had evidence that the women had relationships with Trump, Avenatti said: "Yes".
Cohen, Trump's attorney, paid Daniels US$130,000 (S$170,000) just days before the presidential election in exchange for her silence.
The judge indicated from the bench that he was reluctant to issue the motion for the gag order, but he did not announce a timetable for his ultimate decision.
The hearing Friday comes in the wake of reports earlier this week that Avenatti and Cohen's attorneys had been in discussions for weeks over a possible settlement to the litigation.
The lawsuit also accuses Cohen of defamation over comments he made about Daniels' truthfulness.
Avenatti also said that he has had discussions with Cohen's team about whether the president's former attorney might settle the cases involving him were Cohen to "come clean" about what he has done with Trump.
As he did on Twitter, Avenatti criticized Trump and Cohen for playing games.
"Well they've become justices of the Supreme Court, judges, some of the most important people in America", Dershowitz fired back. Additionally, she is suing the president, arguing a nondisclosure agreement she signed in regard to their alleged affair is invalid because he failed to sign it.
But Michael Cohen's lawyer, Brent Blakely, said that Avenatti's smack talk about Cohen has been over the top, and it could prevent his client from getting a fair trial. "No more lies or lip service", Avenatti tweeted early Friday morning.
Mr Cohen's lawyer, Lanny Davis, cautioned against believing everything that a lawyer says in the heat of a legal battle.