Higgins added: "I spoke to Eddie Hearn yesterday and he said he would be more than happy to help out with opportunities. There are options. I will talk to [American co-promoter] Bob Arum too and there is always the option of fighting in New Zealand again."
Britain's Daily Telegraph this morning reported that Wilder's representatives want to make a fight with Joshua in order to unify all the world heavyweight titles.
"We want to make it public that Deontay wants the fight, and we are prepared to come over, or meet here and get the deal done," American Shelly Finkel said. "Deontay is ready to sign and come to the UK to fight this summer."
If talks between the increasingly erratic Wilder and Joshua, the IBF, WBO and WBA champion, are successful, the pair are likely to sign a two-fight deal, with the re-match in New York or Las Vegas.
Joshua is eager to fight Wilder this year in order to unify the division before he has to deal with his mandatory challenges. Russian Alexander Povetkin, who knocked Englishman David Price unconscious at the Principality Stadium, is the mandatory WBO champion, with Bulgarian Kubrat Pulev next on the list as far as the IBF is concerned.
It remains to be seen how far down the rankings Parker will go after his defeat, the first of his professional career, which followed two successful world title defences.
However, Higgins said the WBO at least were likely to take a sympathetic view after positive talks following the fight. There is no doubt either that Parker has carried himself like a champion in the UK over the past fortnight.
"The sanctioning bodies will view Joe as one of the best quality heavyweights in the world so it shouldn't take too long for him to go up the rankings to become a number one contender as long as he wins his next few. It wouldn't be like starting again."
Another positive is that the New Zealand pay per view figures for Parker v Joshua appear to be very good. "There is confidentiality around it, but it will probably be No1 for revenue if not buys," Higgins said.
The David Tua v Shane Cameron fight in 2009 holds the pay per view record in New Zealand of more than 80,000 buys.
"Joe will get a well-deserved rest and I feel like I've gone 12 rounds myself so I'm going to lay low for a while," said Higgins, who is about to go on a brief European holiday.
Parker is on his way to Auckland for a break with family and friends.
"I'll speak to Joe about what he wants to do. The early indications are that he wants to fight again sooner rather than later."
