Joshua is facing no slouch in Parker: The 26-year-old is unbeaten in 24 fights, though he last knocked out an opponent in 2016, dispatching the noteably chinny veteran Alexander Dimitrenko.
Hearn said: "There have been a lot of rumours that he will join up with us. That's not true, as far as I know", he told Sky.
Over the next three weeks, though, it will intensify as the world heavyweight unification fight nears, and already there appears to be a shift in attitude from the Joshua camp, who believe this could be the first time the Englishman is taken the distance. We've had some conversations. In terms of this, it's new and I think, as I said, I respect the family side because I'm a family man, I respect that all day.
Joshua must first progress past Joseph Parker in a world title unification fight on March 31.
"The fight will be a very exciting fight because I'm prepared, I'm going to come ready, I'm going to be in the best shape and I'm sure you'll do the same".
The resolution of Fury's dispute with UK Anti-Doping has opened the door to his return and, as he sheds much of his excess weight, he is seeking a promoter for his comeback.
"As a heavyweight world champion and a major star in world boxing, [Joshua] should box over here at some stage", Hearn told Sky Sports.
"[Trainer] Brendan Ingle once said, it's easy to beat Tyson Fury, very, very easy. Deontay Wilder, Anthony Joshua, whoever else, I'm coming for you".