The attorneys for Michael Cohen, President Donald Trump’s longtime personal lawyer, are expected to stop representing him in the criminal investigation into his business dealings, according to a person familiar with the matter.

Mr. Cohen’s attorneys are reviewing more than 3.7 million documents federal prosecutors seized in an April raid of Mr. Cohen’s home, office and hotel room to designate which communications they see as protected by attorney-client privilege, ahead of a Friday deadline set by Judge Kimba Wood of the Southern...