"Joseph would fight Tyson Fury next if the terms were right," Higgins told the Herald. "Some would say that would be the wrong fight for Joe next as Fury is a very tricky opponent. We kind of agree. Joe and I regard Tyson Fury as probably the best heavyweight in the world and the man to beat.
"We think he's better than Anthony Joshua and Deontay Wilder. That being said, boxing is a risk and return business. Joe has two young children under the age of two… he has to set up everyone [financially]. Fury v Parker would be a massive global event.
"If the likes of Bob Arum ran it in Vegas it would make big money in the United States but also in the UK because of the background – Joe beat Tyson Fury's cousin Hughie so at the moment is Parker 1, Fury 0.
"There would be massive interest in New Zealand and probably Australia. It would be the biggest global event we've done to date."
Fury's performance in drawing with WBC champion Wilder in Los Angeles late last year after two years out of the ring proved he belongs to be ranked alongside Joshua and Wilder as one of the best heavyweights in the world. His effort to get off the canvas in the 12th round to pour the pressure back on the American had to be seen to be believed and many thought he won the fight.
The 30-year-old Fury, who gets on well with Parker even despite watching his cousin Hughie lose to him in Manchester in 2017, would be a massive challenge for the Kiwi and the Englishman would be a hot favourite if the fight were to be held in the United Kingdom.
A fight in the United States would level the playing field a little for Parker, who has now lost to Joshua and Dillian Whyte – both by unanimous decisions – and that's where promoter Arum and US sports channel ESPN would prefer the fight to be held.
Parker lost his WBO world title to Joshua in Cardiff in 2018 but took home more than $10million and a fight against the self-styled Gypsy King would probably rank as his second highest payday.
"Bob Arum is probably the greatest promoter ever and he's shown he can make deals with anyone; and very tricky deals," Higgins said. "He had a hand in the Thrilla in Manila, Pacquiao v Mayweather… over his career he's made deals with people he likes, hates, trusts and doesn't trust.
"It would have be a substantial amount of money because we see Tyson as far riskier than say Dillian Whyte or Dereck Chisora, which means we'd have to be compensated."
Contrary to media speculation, Higgins had held no conversations with Arum or anyone else about a fight with Fury, but said he would welcome a call.
"They hold the cards, we're not going to chase them. But if they're serious they have my details and they're welcome to open communication."
