U.S. District Judge Kimba Wood has scheduled a hearing in the case for Monday afternoon.
Prosecutors have asked that the seized documents be reviewed for attorney-client privilege by a "filter team" of lawyers within their own office, who would be walled off from the main prosecution team.
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Lawyers for Michael Cohen argued in court on Monday that they could not identify Hannity because he asked that his name not be disclosed in connection with an Federal Bureau of Investigation seizure of Cohen's files. Daniels says she had a sexual relationship with Trump in 2006. Initially, Mueller had requested some records from Cohen while he was with the Trump family company - a position he held for about a decade - yet dropped the request after Cohen pushed back.
Cohen made a similar argument last week.
Cohen has become the central figure in a growing presidential sex scandal, accused of using cash payments and non-disclosure agreements in an attempt to silence Trump accusers such as porn star Stormy Daniels and former Playboy model Karen McDougal. The problem is that Cohen may not know many of those things.
But he said he never retained Cohen "in any traditional sense", never paid him and never got billed for a legal fee.
Donald Trump's personal lawyer is due in court in an extraordinary showdown with United States prosecutors Monday over documents seized in an Federal Bureau of Investigation raid on his home, with a porn star also expected to attend.
In response to Cohen's motion to prevent prosecutors from using evidence collected in Monday's raids of his home and office, the USA attorney in NY asserted the raids were authorized by a federal judge to seek evidence of conduct "for which Cohen is under criminal investigation".
A source familiar with the raids said last week that the information Federal Bureau of Investigation agents were seeking included information about payments to Daniels.
That is despite the Justice Department's creation of an independent team - a "clean team" or a "filter team" separate from the prosecutors and investigators looking into Cohen - to review the material.
Prosecutors are reportedly investigating potential campaign finance law violations by Cohen.
Monday's hearing began with an appearance by porn actress Stormy Daniels, who was swarmed by photographers and almost fell as she was hustled into the courthouse, a scene that captured the sensational atmosphere around the case. In Stewart's case, which also took place in the Southern District of NY, her lawyers successfully objected to federal prosecutors using a "taint team" to review her attorney's files, and the court allowed a neutral special master to review the documents, also allowing Stewart's team to review the documents as well.
Echoing several of Mr. Trump's supporters, the lawyers also noted in their filing that there was "a growing public debate" about whether criminal and congressional investigations by the government "are being undertaken impartially, free of any political bias or partisan motivation".
At issue is who controls the process of winnowing out legal communications from business matters, determining what is relevant to the investigation, and identifying what is privileged and what is unprivileged because it involves crime or fraud - and how long the process takes. He has denied wrongdoing.