Parker defends his title for the second time when he makes his long-awaited UK debut against Fury in Manchester on September 23.
Bellew, a world cruiserweight champion who stunned fellow British heavyweight David Haye last March, is back in training and eyeing his options.
He has ruled out a rematch with Haye. He likes the money involved in a fight with unbeaten world light-heavyweight champion Andre Ward but says Parker's belt tops his list.
