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.