Avenatti said those talks ended last Sunday after "it became clear to me that Michael Cohen was attempting to play a game."
Lanny Davis, a lawyer representing Cohen in connection with a pending federal criminal probe in New York City, had no immediate comment when contacted by CNBC.
Avenatti declined to answer questions about the three other women he says are linked to Trump.
Avenatti said he was awaiting permission from those women to disclose details about their cases.
Otero, during the hearing, seemed sympathetic to Avenatti's arguments that gagging him in the case would be unfair and absurd given the fact that Trump continues to tweet about Cohen and Trump's current lawyer Rudy Giuliani frequently comments to media outlets about Cohen and Daniels.
Otero suggested Cohen's lawyer Brent Blakely did not fully appreciate the significance of asking him to suppress the right of Avenatti to speak publicly.
Referring to Americans' rights of free speech under the Constitution, Otero noted that "those are the most sacred of rights."
Blakely, in asking for the gag on Avenatti, cited the hundreds of Twitter posts made by Daniels' lawyer, as well as his steady stream of media appearances
"You look at the conduct — it's unprecedented," Blakely said.
"At what point does he stop. When does this court say enough is enough."
But Otero, noting Giuliani's recent public condemnations of Cohen for having secretly recorded Trump talking about paying hush money for another alleged mistress, said, "Irony doesn't escape me."
And the judge said Blakely had so far "failed" to make a convincing case for the requested gag.
In addition to holding off on ruling on the gag order request, Otero did not rule on Avenatti's request that the case resume after being put on hold for the past three months.
Proceedings in the case have been suspended because of the existence of the criminal investigation of Cohen in New York.
That probe, Cohen has argued, would prevent him from being able to answer questions fully under oath in Daniels' lawsuit in California.
At his news conference outside of court, Avenatti said he was eager for the stay in the case to be lifted.
"We do not want this case delayed for months or years on end," he said. "It's time to get on with it."
Avenatti also took a shot at Giuliani, who on Thursday night had told CNN that Cohen is "a proven liar,"
"There's no way you're going to bring down the president of the United States on the testimony uncorroborated of a proven liar. I guarantee you this guy is a proven liar," Giuliani had said.
The former New York City mayor was referring to a report that Cohen was willing to tell special counsel Robert Mueller, who is investigating the Trump campaign for possible collusion with Russians interfering in the presidential election, that Trump had known in advance about a planned Trump Tower meeting with campaign officials and Russians who had offered negative information about Hillary Clinton.
Avenatti said of Giuliani: "This guy is an absolute train wreck of a lawyer."
"In fact, I think he's the best lawyer we have working for us in the case," Avenatti added.