Last December in Los Angeles, Fury drew his controversial fight with WBC world champion Deontay Wilder. Fury was knocked down twice, including in the final round, but otherwise was dominant against the American despite his long lay-off with mental health and drug issues.
Parker, still in a rebuilding phase but with on the verge of taking his career to the next level through his multi-fight agreement, has said he is keen to fight Fury, but the self-styled Gypsy King is reluctant to trade blows with a man he considers a good friend.
Parker recently missed the birth of his third daughter, Michaela Florence, and told the Herald he was keen on getting back in the ring after the longest lay-off in his professional career. He last fought in December, a knockout win over Alexander Flores in Christchurch.
"We're hoping to be fighting next month or July," he said. "But I'm hoping it's next month. It will be nice to have a fight and get back in the swing of things – I'm in great shape, the best shape I've been coming into camp ever.
"I'm a bit more serious about training and keeping in shape during my off time. That's very beneficial coming into camp. I still don't know what's happening [in terms of next fight] but at least I'm starting in the right place – I don't have to lose a lot of weight. I'm enjoying training… before there used to be a lot of volume due to the weight issues. But now we're actually able to focus on things I need to focus on."