"I wouldn't say we were close to that but there were moments where David and Joseph were saying things.
"Many fighters in Anthony's position would have turned around and gone nah β¦ tell him to jog on," Hearn told Watson.
He didn't disclose what Parker and Higgins said, but before the fight was announced Parker's team took multiple jabs at the British boxer.
Parker and his team set about rattling Joshua's cage via social media, shining a light on what they describe as Joshua's "glass chin" in particular.
Before both fighters finalised their contracts for the fight, Parker told the Telegraph his "sole mission is to smash to bits the man with the glass chin".
"All we have said is that Joshua has a glass chin," Parker said.
"We know it, he knows it, everybody knows it, they just don't talk about it.
"We saw him get dropped by Wladimir Klitschko but he still had the heart to get up and finish the fight β I'll give him that β but if I catch him and hurt him I'm not going to give him the chance to recover."
In November last year Parker called out Joshua on Twitter, saying he'd like to take his two world title belts off his hands.
"My belt's never for sale but I'll add your two to my collection when you're ready," it read.
Joshua returned suit replying: "Sips tea, continues to read tweets & refreshes email... Still No Offer."
On one occasion Parker went as far to call Joshua the "king of steroids" before retracting that statement.
Higgins also compared Joshua to the English football team.
"We have a hypothesis that Joshua is like the English football team. Built up and hyped up, but never steps up when it gets to the top level," Higgins told Behind the Gloves.
"They will get up to the football world cup finals, but never make the final because they choke.
"So we wonder whether Joshua at unification level will be found out?"
However, Hearn did admit that sledging is something boxing fans like to see before a fight.
He said the "niggles are good, the niggles are fun" and that the fans love watching fighters attack each other verbally.
"We like the talk and we welcome it.
"I feel like there's going to be plenty more from Higgins in this build up," he told Watson.
The fight will take place at Millennium Stadium on April 1 (NZT), with Parker's WBO belt and Joshua's IBF and WBA belts on the line.
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