The U.S. Attorney's office in Manhattan made the filing after lawyers for Cohen and Trump asked a judge to block the Justice Department from reviewing records seized Monday in Federal Bureau of Investigation raids on Cohen's apartment, hotel room, office and safety deposit box.
The raids enraged Trump, who called them an "attack on the country".
A lawyer for President Donald Trump sought in court on Friday to stop USA prosecutors from deciding what materials seized from his personal attorney can be used in a probe that began with a referral by investigators looking into Russian meddling in the 2016 presidential election.
On Monday, the Federal Bureau of Investigation seized electronics and documents, including Cohen's communications with his clients.
The interest in Cohen's communications with Trump suggests that the investigation is delving into the president's actions, legal experts said.
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Facebook was accused of unwittingly sharing information of more than 87 million of its users with the company, per NBC News . Wozniak's comments echoed those of Apple CEO Tim Cook in an interview that aired on MSNBC last Friday.
Investigators also sought any communications Cohen had with Trump and campaign aides about "potential sources of negative publicity" in the lead-up to the election, the person said. The lawyers said they should be allowed to identify which of the documents are protected by attorney-client privilege before prosecutors get to look at them.
Cohen has been accused of making an in-kind contribution to Trump's campaign by paying Clifford with his own money in order to benefit the president's run for office.
Trump repeatedly denounced the raids as disgraceful..
Michael Avenatti, the attorney for Trump love interest/porn star Stormy Daniels, also appeared at the courthouse asking to address the court Friday afternoon. He told Wood he had every reason to think some of the documents involved his client, and he asked to be heard when the hearing reconvenes.
McDougal was paid $150,000 in the summer of 2016 by the parent company of the National Enquirer under an agreement that gave it the exclusive rights to her story, which it never published.
The White House has consistently said Trump denies either affair.