Trump is incensed by the raid and seething with anger.
Rumors continue to swirl whether Trump will fire Mueller or Rod Rosenstein, but so far the White House has not confirmed that.
The special counsel and an attorney for Cohen did not immediately respond to requests for comment.
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.
Cohen has been referred to at different times as Trump's fixer, "pit bull", and consigliere. And they help explain why Mr. Trump was furious about the raid. Trump, a Republican, sent his own lawyer to a hastily arranged hearing before a federal judge in Manhattan to argue that some of the records and communications seized were confidential attorney-client communications and therefore were off-limits to investigators.
"Although Cohen is an attorney, he also has several other business interests and sources of income". "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.
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One of the sources said the warrant also referenced an investigation into wire fraud and bank fraud. He has called the raids "inappropriate and unnecessary" and said prosecutors improperly obtained privileged information.
The revelation that investigators are interested in finding out more about the "Access Hollywood" tape indicates they are focused on what role, if any, Cohen played to protect his client during Trump's presidential campaign.
Trump "is the President of the United States", Hendon said.
Of Trump, McKay said: "His attorney-client privilege is no greater than any other person who seeks legal advice".
In addition to seizing documents related to women who claimed to have affairs with the president, investigators were also looking for records relating to the infamous "Access Hollywood" tape.
The Access Hollywood tape became public a month before the election. Time magazine has reported that Cohen a 51-year-old lawyer was a man who was a confidant of the president and probably handled all the payments to Stormy Daniels. Both women say they had affairs with Trump.