Higgins will on Wednesday outline the latest developments in negotiations for a unification fight between WBO champion Parker and Joshua, who holds the IBF and WBA belts.
Team Parker will also continue their claims around Joshua's supposed "glass jaw" and plan to produce video evidence of him being repeatedly taken to the canvas.
"There is a lot of hype and glamour. But we believe Joshua will fold at unification level like England fail to reach World Cup finals," Higgins told the Daily Mail.
Higgins is in talks with Joshua promoter Eddie Hearns about a super fight in the UK in early 2018. While Parker has shown a willingness to reduce his share of the purse to 35 per cent, it's understood they were still some way off what Hearn considered fair, constantly questioning the Kiwi's marketability and value.
Deontay Wilder, the third fighter in the heavyweight champion equation with the WBC belt, is the other option with both Parker and Joshua in talks with the outspoken American.
Joshua remains Parker's preference though.
"People have been asking why we don't make a unification fight with Deontay Wilder. For us it's simple: Anthony Joshua is the softer of the two," Higgins said.
"So taking the softer of the two first makes sense."
Parker's trainer Kevin Barry continued the big talk with FightTalk.net, saying he believed Joshua was there for the taking. He discussed the Brit's robotic style and lack of stamina before delivering a crushing blow.
"The biggest chink in his armour out of everything is… I believe he has a suspect chin," Barry said.
"You look at the names and the people he has fought it's no wonder that chin hasn't been exposed a lot more. We know he was knocked out in the amateurs, we know he's been knocked out in the gym sparring, we know an old 40-year-old Klitschko had him down.
"I can promise you this, when Joseph Parker has Anthony Joshua hurt and down in the fight, the fight would be over! We would never let him recover!
"We seriously want to make this fight; Joseph Parker knocks Anthony Joshua out. We will wear his belts."
Meanwhile, Parker isn't interested in being a late opponent for Tony Bellew after the Brit's December 17 rematch with David Haye fell through when Haye injured an arm, tripping down some stairs.
Bellew has been challenged by Tyson Fury and Dillian Whyte since Haye's withdrawal, but he insists that WBO heavyweight champion Parker was the only viable alternative.
Bellew, a pumped up cruiserweight has always seen Parker as vulnerable and the two have long eyed a potential fight. There was talk of Parker fighting the winner of Bellew v Haye to boost his British profile.
But Parker's hopes of bigger things around a unification fight seem to have put that on the back-burner.
"This week, we've contacted Joseph Parker but he's not available, he said he isn't ready for December 17. He was the only one who made sense. I thought he might take it, because he's recently come off a win over Hughie Fury. It's not going to happen," Bellew, who is also promoted by Hearn, lamented on Sky Sports UK.
There are no gains for Parker taking that fight on late notice. he has only just started a training camp in Auckland that is based around fitness and weight loss rather than fight skills.
Parker hopes to use the camp to springboard him into a 2018 champaign he believes can prove his ability at the very top.
Photo by: REUTERS. Caption: Anthony Joshua continues to dominate the world heavyweight market that is heating up.