CNBC reported Tuesday that Cohen has been telling friends he expects to be arrested soon, citing two different sources.
ABC quoted sources with knowledge of Cohen's legal team abandoning him after losing an attempt in court for secrecy regarding the investigation into documents seized by the FBI from Cohen.
ABC concluded, "this development, which is believed to be imminent, will likely hit the White House, family members, staffers and counsels hard."
Late last week, a federal judge said Trump should publicly file his objections to findings of a court-appointed special master reviewing documents seized in a probe of the business dealings of his longtime personal lawyer, Michael Cohen.
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In an order issued on Friday, U.S. District Judge Kimba Wood in Manhattan rejected efforts by Trump, the Trump Organization and Cohen to file their objections entirely under seal.
She agreed with the government that the filings should be public except as to portions that "divulge the substance of the contested documents."
Wood said she would decide later which portions could be sealed.
Joanna Hendon, a lawyer for Trump, did not immediately respond to requests for comment. Todd Harrison, a lawyer for Cohen, did not immediately respond to similar requests.
The criminal probe into Cohen's business dealings stems in part from a referral by Special Counsel Robert Mueller, who is investigating whether Trump's 2016 campaign colluded with Russia to influence that year's U.S. presidential election.
Trump has repeatedly said there was no collusion, and Russia has denied interference. Cohen has not been criminally charged.
The special master, former federal judge Barbara Jones, is reviewing materials seized in April raids of Cohen's home, office and hotel room, to determine which are subject to attorney-client privilege.
On Monday, she said in a report that 162 files, out of more than 292,000 reviewed so far, were privileged or partially privileged, and seven were "highly personal."
Roughly 3.7 million files were seized, Cohen's lawyers have said. Jones is reviewing only those that lawyers for Trump, the Trump Organization and Cohen believe might be privileged.
The case is Cohen v U.S., U.S. District Court, Southern District of New York, No. 18-mj-03161.