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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

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