They also argue that Daniels, too, would be prejudiced, because, they write, she "likely would be unable to obtain the documents and deposition testimony that she is seeking from Mr. Cohen" - presumably because he would invoke the Fifth Amendment privilege.
Cohen, who is under criminal investigation for possible bank fraud and campaign finance violations, has come under scrutiny by federal prosecutors for his efforts to tamp down negative stories about Trump.
Trump's anger at the probe has intensified, with him musing publicly about firing Mueller and the man who authorized the probe, Deputy Attorney General Rod Rosenstein.
U.S. District Judge Kimba Wood on Monday will consider Trump's extraordinary request to let the president's attorneys conduct the document review for information protected by attorney-client privilege before Justice Department lawyers can look at it.
The judge asked the opposing attorneys to submit a joint proposal with four names for a potential special master, whom the judge said "could have some role" in sorting through the seized documents and determining what was privileged. Daniels, who has been talking openly about what she says was her liaison with Trump, is suing to get out of the agreement.
Prosecutors fired back in their own filings that appointing a third party would "mark a serious departure from the accepted normal practices of this district".
Prosecutors have asked that the 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.
The hearing will be Cohen's first appearance before a judge since the Justice Department revealed in court documents on Friday that he is the subject of a months-long criminal investigation. But it's pretty hilarious that everyone associated with Michael Cohen now has to say Just to be clear, Cohen never negotiated hush money for any porn stars or Playboy models on my behalf.
"The attorney-client privilege is hugely important, and prosecutors and judges take it extremely seriously, but it is narrow", Rocah said.
Hannity later said that Cohen never represented him in any matter, though they had some "brief discussions" about legal issues. Does attorney-client privilege apply to communications between the two? "I never paid legal fees to Michael", Hannity said. "And he's going to continue focusing and fighting for the American people".
"Michael would very generously give me his time", Hannity said.
Ms Daniels is now involved in a separate civil case against Cohen and President Trump, suing for defamation after they denied the $130,000 payment in 2016 was to keep her silence about the alleged extra marital affair with President Trump.
President Trump has over 50 million followers and his statements make instant headlines in nearly every country.
Attorney Joanna Hendon representing President Trump, center, leaves the federal court, Friday, April 13, 2018, in NY. Gasps could be heard echoing throughout Wood's stately, large courtroom. "The president trusted Mr. Cohen as his fixer for years".
A fiery appearance by Donald Trump's alleged former mistress, and an embarrassing revelation about a close journalist friend of the president have overshadowed day one of an important court case that threatens a U.S. political showdown. "He's played by a different set of rules, or should we say no rules at all".