WBA and IBF champion Joshua will be looking to take Parker’s WBO title in next month’s mouthwatering heavyweight fight.
The two giants will go head-to-head in Cardiff on March 31 and both are currently going through their gruelling training camps in preparation.
Joshua has sent a warning to his opponent, insisting the New Zealander must arrive at the Principality Stadium in perfect shape.
And the 28-year-old Londoner hopes Parker won’t disappoint the awaiting fans by taking to the ring undercooked.
Joshua told Sky Sports: “I hope he’s training well, I hope he’s fit.
“People will wait ten, twelve weeks for us to come together and no one wants to [see him] lay down in the first or second round.
Anthony Joshua ring girl Sara Beverley Jones
“I hope he’s fit and ready for a good fight because I am”
“I hope he’s fit and ready for a good fight because I am.”
Parker’s promoter David Higgins claimed earlier this week that his star will be more than ready for his meeting with Joshua.
Higgins said: “He won’t be fazed at all. To him, it will be another boxing ring. There might be some people that might be overawed, but Joseph Parker is not one of them.
“Whether it’s in the North Pole or Timbuktu, or the Millennium Stadium, the preparation will be the same, the mindset will be the same.
“One thing we know about Joseph is that side of it won’t faze him. He’s got a job to do, he knows what it is, he’ll take it very seriously.
“There might be some people that might be overawed, but Joseph Parker is not one of them.”
Joshua beat France’s Carlos Takam in the tenth round of their fight in Cardiff last October.
Parker, meanwhile, claimed a majority decision win over Tyson Fury’s cousin Hughie in Manchester in September.