Fury's trainer and father Peter has said in an interview with BoxNation that he rates 25-year-old Parker extremely highly and that while Hughie, 22, has improved greatly since recovering from a skin condition, he will have to be at his best to win.
The fight, slated for April 1 after Parker's promoters Duco Events won the purse bid against Fury's promoter Frank Warren, will probably be held at Auckland's Vector Arena, but Singapore and even Manchester remain options.
A Duco spokesman said there was unlikely to be an announcement this week.