"My body type, even though it's not really muscular, [has] worked for us," Parker told Sky Sports UK. "We know that we can fight hard from round one to round 12. It's all that matters."
Joshua, 28, is hard at work at his camp in Sheffield and has posted pictures on social media of his heavily-muscled body.
Parker, laughed at by Joshua for his "pie-eating" physique, said: "When you watch him, when you see all the training, it's like they are doing all this new training and it looks really hard, and it looks intense, and it looks the type of training that will prepare you for 12 rounds.
"But, in saying that, just maybe their team need to work on a few things. We know that our team has a good structure and a good training programme that will allow us to fight 12 rounds, if we need it.
"But I'm not sure why he tires, that's something he has to sort of figure out."
Parker is now into the sparring phase of his preparation at his Las Vegas base, with Barry telling the Herald recently that the weight put on following his points victory over Hughie Fury in Manchester last September is coming off and that he was looking as sharp as ever.
He and Barry would have liked to have finished his recent fights in more spectacular fashion, but going 12 rounds against Fury and Razvan Cojanu last year, and Andy Ruiz and Carlos Takam in 2016, have at least shown Parker has good endurance.
Many believe the Joshua v Parker fight will go to the late rounds, and it's here that the New Zealander could have an advantage.
"I see videos posted everywhere of him [Joshua] doing the most sophisticated, new-age training methods that man has ever seen and, yet he's looked very tired in his last couple of fights," Barry told Sky Sports UK.
"Every time he's been asked to go on to the later rounds, he's really struggled so that's a question for his training staff.
"He wouldn't want to be slowing against Joe, because I can promise you this. Joe will be coming on in the later rounds."
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