The lawyer said that Daniels, whose real name is Stephanie Clifford, did not get a reply to a letter offering to return the money she received as part of the nondisclosure deal, Bloomberg News reported.
"We do not believe it is appropriate for her to preside over this case, which obviously involves the president, in light of this fact", said Michael Avenatti, who represents Daniels.
Trump's attorney, Michael Cohen, has not immediately returned messages for comment.
But Avenatti revealed in a tweet on Tuesday, that Trump and Cohen had missed the deadline to revoke the contract.
While Daniels' lawyer has said Trump knew about the payment and had a sexual relationship with the actress (which the actress herself previously denied), Daniels has not explicitly spoken out about the alleged affair outside of the lawsuit filings.
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Avenatti in a letter to Cohen, a copy of which was seen by Reuters, said the actress would wire the funds to an account of Trump's choosing by Friday.
A lawyer for Daniels, whose legal name is Stephanie Clifford, reportedly put in the request on Friday, claiming that because Judge Elizabeth Feffer of Los Angeles Superior Court is now seeking a federal appointment, it would not be appropriate for her to make a judgment in a case involving the president. She reportedly taped an interview with CBS's 60 Minutes during which she made new claims about Trump.
Following initial reports of Cohen's payment to Daniels, Cohen said Trump "vehemently denies" any affair.
Clifford could be subjected to a $1 million penalty if she broke the nondisclosure agreement she signed. "Time to buckle up". Neither Cohen, nor his lawyer, Lawrence Rosen, responded to a request for comment.
Daniels signed a non-disclosure agreement in October 2016 which she says was to keep her quiet about her tryst with Trump, but the notary public-who is in Texas as Daniels owns a home in Forney-only stamped the document and failed to also sign and date it as required. Avenatti told CNN over the weekend that at least 10 people had offered to pay the penalty if she would discuss the alleged affair.