"There is a lot of hype and glamour [around Joshua]," Higgins told the Daily Mail.
"But we believe Joshua will fold at unification level like England fail to reach World Cup finals."
The 25-year-old Parker wants a 40 per cent share of the purse against Joshua, with revenue shared rather than a fixed fee, but has said he would accept 35 per cent just to get the fight made.
A unification fight between the pair could happen as early as March, with the revenue undecided but likely Wembley or Cardiff's Principality Stadium. Joshua also has close connections in Dubai, so a fight in the Middle East wouldn't be out of the question either.
Trainer Barry continued a theme in an interview with Fight Talk, when he called the Englishman "robotic" and "predictable", adding: "The biggest chink in [Joshua's] armour out of everything is... I believe he has a suspect chin.
"You look at the names and the people he has fought and it's no wonder that chin hasn't been exposed a lot more. Look mate, 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."
Joshua has won all of his 20 professional fights by knockout, but was rocked by a left hook by Dillian Whyte and Klitschko sent him to the canvas in their epic fight at Wembley in April.
Parker is undefeated over 24 professional fights. He has won 18 by stoppage.