“Mr Cohen is fully cooperating with the Southern District of New York and is offering more information that he’s now discovered when he retrieved back his cell phones and other documents from the Southern District,” Lanny Davies told MSNBC on Tuesday.
“He also has additional information for the Southern District involving criminal behaviour that needs to be looked into.”
Prosecutors at the Southern District of New York are currently investigating the president over possible corruption related to his inauguration spending, as well as hush money payments given to two women who claim they had affairs with Mr Trump.
Cohen was sentenced last year to three years in prison, partly for his role in hush money payments to one of the women, former porn star Stormy Daniels. He is scheduled to report to jail next month.
In February, Cohen provided during public testimony to Congress two $35,000 (£26,600) cheques which he said were reimbursements for $130,000 (£102,700) he gave to Ms Daniels before the 2016 presidential election.
One of the cheques was signed by Mr Trump, the other by the president’s eldest son, Don Jr, and the Trump Organization’s chief financial officer Allen Weisselberg.
“The writing of the $35,000 cheque signed by Donald Trump is evidence of a crime of conspiracy to violate the very crime federal prosecutors said was directed by President Trump,” Mr Davies said.
He added: “Donald Jr is not president, neither is Mr Weisselberg, why have they not been indicted?”
Despite the payments to the two women, Mr Trump has denied the alleged affairs and insists the arrangements do not violate campaign finance laws.
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