Cohen is due to report for his three-year prison sentence on March 13, but not without appearing for three hearings on Capitol Hill.
Cohen originally agreed to publicly appear before the House Oversight Committee on February 7, but postponed his testimony due to safety concerns caused by alleged "ongoing threats" against his family by Trump.
CNN reported Monday, however, that lawyers for Cohen are "in discussions" for him to provide his previously agreed-upon public testimony if his safety can be guaranteed.
Cohen is also expected to testify before the House and Senate intelligence committees in closed-door sessions on February 8 and February 12, respectively.
In August, Cohen pleaded guilty to tax fraud, bank fraud, and campaign-finance violations in the Southern District of New York. The violations were related to payments to buy the silence of two women, Karen McDougal and Stormy Daniels, who say they had affairs with Trump.
Federal prosecutors said in their sentencing memo for Cohen that he made the payments "in coordination with and at the direction of" an individual widely believed to be Trump, making him an unindicted co-conspirator in the case.
On November 30, Cohen struck a deal to plead guilty to one count of lying to Congress in exchange for cooperating with Mueller. He admitted to lying to lawmakers about the Trump Tower Moscow deal, and people close to him have said he intends to set the record straight during his closed-door testimony before the congressional intelligence committees this month.