Parker, training at his Las Vegas base for the fight against Fury which will probably be held at Auckland's Vector Arena on May 6, has already indicated his willingness to fight Bellew, a cruiserweight who went up a weight class to shock Haye and most pundits with an 11th-round stoppage.
Haye was originally slated to challenge for Parker's title due to his WBO ranking, but opted instead for what would have been a more lucrative fight against Bellew, whom he would have seen as an easier opponent.
The former two-time world champion at cruiserweight and heavyweight injured his Achilles during the fight and at 36 his future must be in doubt.
A victory over Fury would lift Parker's profile in the UK considerably, a potential boon given the explosion in the popularity of heavyweight boxing there. A British newspaper reported that 700,000 pay per view packages were sold for the Haye v Bellew fight in the UK.
"The best way to raise his profile in the UK is to beat Englishmen, starting with Fury," Higgins said. "If we hold the fight in Auckland, that would mean it would screen at about 11am on a Saturday in the UK and we have some strong interest from Sky Sport UK and also ITV."
Most pundits, including this one, would predict a victory for Parker over Bellew given his speed, power and technical ability. Bellew would have been down on the judges' scorecards against the relatively slow Haye until Haye's injury in the sixth round.