Joseph Parker has arrived back in the country and is getting right back to training following Sunday's heavyweight title fight against Anthony Joshua.

Parker lost his WBO title in the defeat by unanimous decision in Cardiff but is already looking ahead to his next step in the ring.

"When does training start? Tomorrow. I'll go for a run. Now that I'm in good shape, I don't want to waste it. We want to relax and enjoy ourselves and look forward to the future. We want to plan some fights and get into it straight away," Parker said after arriving at Auckland Airport.

"Kevin [trainer Kevin Barry] and I deserve a break. The whole team deserve a break. We want to plan and sit down and see what options we have and then go from there." 

"It's always great to come home. It's something I've been looking forward to for a while. I've been in Vegas and in London. We had a great fight but it's always good to be home."

Talk has already begun about what is next for the Kiwi fighter.

Parker's promoter David Higgins said yesterday the New Zealand heavyweight could be open to fighting on a Joshua undercard after his recent points defeat to the Englishman.

A day after Joshua relieved Parker of his WBO world title belt, trainer Kevin Barry suggested his man could fight as early as August in the United Kingdom, and that time frame would fit in with the latest news American Wilder is willing to put his WBC title on the line against Joshua in a few months' time.

"We saw what a big deal the Povetkin-Price fight was as the main undercard fight to Parker-Joshua, and a Joshua show has a massive audience," Higgins told the Herald. "It's about leaving ego out of it."

Asked about an August time-frame, Higgins said: "August would be about the right time in the UK. Joe has got respect and support in the UK now whereas previously his only market was in New Zealand."

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."