Lanny Davis, who was hired by Mr Cohen last month, told National Public Radio Mr Trump's former attorney would "never" accept a pardon from "a man that he considers to be a corrupt and a dangerous person".
The unexpected statement comes as yet another blow to Mr Trump's chances of extricating himself from what is developing into a legal minefield.
On Tuesday, Mr Cohen pleaded guilty to eight charges, including to campaign finance violations that may put Mr Trump in legal jeopardy.
Mr Cohen, one of Mr Trump’s closest associates for more than a decade, said he arranged to make payments “for [the] principal purpose of influencing the election” at the direction of a “candidate” for federal office. He did not give the candidate’s name, although he was working for Mr Trump at the time.
The president is alleged to have attempted to buy the silence of two women he is accused of having extramarital relationships with.
Many pundits saw a pardon for Mr Cohen as one of Mr Trump's best chances of keeping his former lawyer from further revealing the inner workings of his campaign and subsequent period in the White House.
"He has flatly authorised me to say under no circumstances would he accept a pardon from Mr Trump, who uses the pardon power in a way that no president in American history has ever used," Mr Davis said.
He accused Mr Trump of using the power to "relieve people of guilt" for "political cronies" who "committed crimes", adding, "Mr Cohen is not interested in being dirtied by a pardon from such a man".
Mr Davis said Mr Trump directed Mr Cohen to commit campaign finance laws, meaning he was "guilty of a crime" that was "far beyond what has classically been called impeachable offences".
“The president of the United States is a criminal," he continued. "He has not plead guilty to a crime but his own lawyers have described him directing somebody to do something that is a criminal act, which is to hush up his affairs with two women, and that’s not what this is about, it’s about his hushing up those affairs in order to influence the outcome of an election."
In a New York court on Tuesday, Mr Cohen told a judge he was aware of what he was doing before pleading guilty to the charges, admitting that he worked “at the direction of" Mr Trump when he attempted to buy the silence of Karen McDougal, a former Playboy playmate who claims she had an affair with the president in 2016.
Mr Cohen also admitted he worked “with and at the direction of the same candidate” to deliver a $130,000 (£100,000) payment to adult film actress Stormy Daniels to silence her claims about an affair.
In the NPR interview on Wednesday morning, Mr Davis again raised the possibility of Mr Cohen providing information that would be "of interest" to Robert Mueller, the special counsel investigating possible links between the Trump campaign and Russia.