Federal agents seized records on a variety of subjects in raids Monday on Cohen's Manhattan office, apartment and hotel room, including payments that were made in 2016 to women who might have damaging information about Trump.
The search warrant executed Monday sought all of Cohen's communications about payments or negotiations with adult-film star Stormy Daniels and ex-Playboy model Karen McDougal.
The investigation is being run by Robert Khuzami, a veteran federal prosecutor whose boss, Geoffrey Berman, is the interim USA attorney for the Southern District of NY.
The corridors of power in the White House and the United States are agog with rumors.
The president Tuesday continued his attacks on the Justice Department, tweeting: "Much of the bad blood with Russia is caused by the Fake & Corrupt Russia Investigation ..."
As the president's right-hand man, Cohen also has intimate knowledge of some of Trump's most closely guarded secrets related to his personal conduct and financial dealings.
Cohen is also being investigated for bank fraud and improper campaign donations. The news agency said it was unclear whether Mueller's investigators have evidence that Cohen met with a prominent Russian, as the dossier claimed. "If they're specifically going after communications between the president and Cohen, it confirms the investigation does relate to the president in some way", said Randall Eliason, who teaches white-collar criminal law at George Washington University Law School. He has called the raids "inappropriate and unnecessary" and said prosecutors improperly obtained privileged information. There were no other women beyond Daniels and McDougal named in the warrant in regard to the President, the source said. The feds could be looking into whether Cohen tried to use illegal tactics to try and keep the "Access Hollywood" tape from reaching the public.
A subpoena is more typical, to protect attorney-client privilege.
The interest in Cohen's communications with Trump suggests that the investigation is delving into the president's actions, legal experts said.
The details in court papers came as lawyers for Cohen and Trump sought to block the Department of Justice from examining records and electronic devices, including two cellphones, seized by the Federal Bureau of Investigation on Monday from Cohen's residences, office and safety deposit box. Both women say they had affairs with Trump.