An inmate is understood to have died when he fell from a landing at the jail.
The man is thought to have died at HMP Altcourse in Fazakarley, Merseyside, at about 12:00 GMT.
HMP Altcourse director Steve Williams said the unnamed prisoner's next-of-kin had been informed.
Mr Williams then added: "As with any death in custody, this will be investigated by the Prison and Probation Ombudsman."
The G4S-run prison was the first privately financed and managed jail in the UK.
HMP Altcourse is a Category B prison, which caters for about 1,300 male prisoners.