Lawyers for Michael Cohen, President Donald Trump’s former personal lawyer, asked a federal judge in a memorandum filed late Friday night to impose no prison time for Mr. Cohen at his scheduled sentencing later this month, citing Mr. Cohen’s contrition and his cooperation with law enforcement.

In their plea for leniency, Mr. Cohen’s lawyers said Mr. Cohen’s decision to cooperate with investigators reflected his “personal resolve, notwithstanding past errors, to re-point his internal compass true north toward a productive,...