Diddy Requests to Serve Prison Sentence at Fort Dix

10/7 12:41 PM PT -- Federal prosecutors just responded to Diddy's request to serve his sentence at FCI Fort Dix and they say they take "no position."

Diddy's got a preferred prison in mind for where he wants to serve out the remainder of his 50-month sentence ... and it's FCI Fort Dix.

Teny Geragos, one of the attorneys who represented Diddy in his criminal trial, fired off a letter, obtained by TMZ, Monday to Judge Arun Subramanian ... asking the court to recommend to the Bureau of Prisons that Diddy be shipped off to the low security federal correctional institution in New Jersey.

Diddy's legal team says FCI Fort Dix is the best landing spot for Diddy because there he can "address drug abuse issues" and "maximize family visitation and rehabilitative efforts."

Teny's father and longtime Diddy attorney Mark Geragos previously told Harvey on the "2 Angry Men" podcast Diddy will have a target on his back wherever he ends up. Diddy's attorneys told the judge Friday at sentencing someone already planned to shank him in jail.

Other celebs who have done hard time at FCI Fort Dix include 'RHONJ' stars Teresa and Joe Giudice.

Judge Subramanian can recommend a prison for Diddy as well -- it doesn't have to be Fort Dix -- but ultimately the Bureau of Prisons has the final say.

Diddy's been locked up for over a year at MDC Brooklyn, and he will call federal prison home for more than 2 years ... and it will be interesting to see if the BOP agrees with his lawyer's recommendation, or if the feds ship Diddy off somewhere else.

BTW, we checked ... herbal oil and prayer oil are available, but there's no baby oil in the Ft. Dix commissary, although baby powder is available.