The 56-year-old had been released on Sunday to attend an appointment but failed to return to the high security jail when expected.
His offences include murder, indecent assaults and cruelty to children.
He was originally jailed in 1989 for murdering his niece Sue Ellen.
Clifford raped and strangled the eight-year-old, before leaving her on a deserted railway line in 1988.
He was freed in 2005 but thrown back behind bars in 2007 for breaching the terms of his probation.
Inspector Paul Noble said: “We have initiated enquiries to locate John Clifford.
“He is described as being 1.75m tall with green eyes and fair hair.
“He is of medium build with a fresh complexion.
“When last seen he was wearing a black beanie style hat, heavy black coat, grey trousers and black dress shoes.
“He was last seen using a distinctive three-wheel mobility scooter bearing the registration plate EXZ 4974.
“Members of the public or anyone with information about his whereabouts should contact us immediately on 101.”
The Prison Service said: “We are investigating the circumstances surrounding the abscondment of John Clifford.
“At this time we are focused on returning him to custody and we would ask anyone with information to contact the PSNI immediately.”
If you see anyone matching this description please call your nearest police station or contact Crimestoppers on 0800 555 111.