Federal prosecutors are full steam ahead to lock up Diddy … asking a judge to sentence him to more than 11 years in prison following his conviction on prostitution-related charges.

In a new court filing — obtained by TMZ — prosecutors say they want “at least 135 months’ imprisonment” for Diddy, along with a $500k fine.

Judge Arun Subramanian is set to hand down Diddy’s sentence on Friday in NYC.

The hip-hop mogul is currently facing a max of 20 years in prison after being found guilty on two counts of transporting male prostitutes across state lines … where they engaged in “freak-offs” that became a centerpiece of his criminal trial.

Prosecutors says Diddy’s crimes are “serious” and note similar cases have led to sentences of more than 10 years for defendants who, like him, used violence and put others at fear.