Lawrence Phillips -- Ex-NFL RB Suspected of Killing Prison Cellmate

Ex-NFL running back Lawrence Phillips -- the 6th overall pick in the 1996 NFL Draft -- has been named a suspect in the murder of his prison cellmate ... officials confirm.

The 39-year-old -- who played for the Rams, Dolphins and 49ers -- is serving time at Kern Valley State Prison in California ... on a 31-year sentence for all sorts of convictions, including spousal abuse.

Officials say Philips' cellmate -- 37-year-old Damion Soward -- was found in his cell around 1AM on Saturday. Soward had been locked up on a 1st degree murder conviction.

Officials say there was ANOTHER murder in the prison on the same day -- and that victim's cellmate is also the main suspect in that case. Unclear if the two murders are linked.