The Justice Department said Friday that Cohen is part of a criminal investigation.
Representing Trump, Joanna Hendon said that as Cohen's client, Trump has the right to assert what's privileged, not Cohen.
Federal agents raided Cohen's Manhattan office and residence on Monday, seizing records on topics, including a $130,000 payment made to porn actress Stormy Daniels.
The raids were conducted after federal prosecutors in Manhattan obtained a search warrant based, in part, on a referral from special counsel Robert Mueller, who is conducting the federal probe into ties between Trump campaign associates and Russian Federation. She argued that materials obtained from Cohen had to be handled carefully because some could relate to a sitting president.
Michael Cohen, President Donald Trump's maybe-current, maybe-former personal attorney, is having a nice Friday afternoon, smoking cigars on a Manhattan bench with his friends on the first truly lovely day in New York City in months.
Investigators are said to have sought additional records related to a 2005 "Access Hollywood" tape featuring Trump in an effort to determine whether, and to what extent, Cohen tried to quash damaging information about the president during the election.
Whatever the judge decided, Hendon said, would have to "withstand scrutiny for all time".
CBO report projects massive deficits during Trump administration
Real GDP will grow by 3.3% in 2018; 2.4% in 2019; and 1.8% in 2020, it said. In our projections, budget deficits continue increasing after 2018.
"If you are looking for evidence, you can't do any better than people talking on tape", said Mr Nick Akerman, a former prosecutor in the 1970s Watergate scandal that brought down then President Richard Nixon. "... He is the President of the United States".
Zeldin said a conversation between attorneys for different clients would most likely not be considered covered by attorney-client privilege.
Wood requested the attorneys to reconvene in the future Friday. Wood also heard arguments on how to keep the names of "innocent individuals" out of the public legal fight.
Michael Avenatti, attorney for Stormy Daniels, outside the Daniel P. Moynihan Courthouse in Manhattan today.
Cohen, however, said the officials who conducted the raid had been courteous and professional.
Accordingly, they argue, most of the material seized by the Federal Bureau of Investigation does not involve attorney-client privilege and could figure in a future court case. Defense attorneys typically advise clients under investigation to avoid speaking with one another. According to Avenatti, the issue was an even more discrete set of clients-only those who had retained Cohen, but who had never been part of a proceeding or discussed with third parties.