Joshua, the IBF and now WBA holder after his epic victory over Wladimir Klitschko at Wembley in April, faces a rematch against the Ukraine and then a mandatory defence against Bulgarian Kubrat Pulev should he retain his belts.
A blockbusting unification fight against Parker - possibly at Wembley - would then await the pair in the next Northern Hemisphere summer.
Hearn, now a major powerbroker in the global heavyweight scene, said: "I like David Higgins. I think Duco have a good opportunity in fighting Hughie Fury. It's a fight, I think if it happens, that they should win and then I would stay here to be honest with you. I would try and knock off all the guys that would make my profile so significant that the Anthony Joshua fight becomes a huge UK and worldwide event.
"Certainly victories over Hughie Fury and Tony Bellew or Dillian Whyte would put Joseph in a brilliant position to earn a lot, a lot of money in the Anthony Joshua fight and put him in a position where that fight is a necessity rather than a potential fight.
"Obviously we're both blessed to have heavyweight champions that we represent and obviously at some stage they're going to fight each other.
"We want to make sure the next guy they fight next is one of our [Matchroom] guys and that is Dillian Whyte, Tony Bellew or Anthony Joshua. It's important that we stay close to each other and it's important that we strategise together on the way forward.
"We don't know whether the Hughie Fury fight will happen, the jury is still out on that one, and if it doesn't I think Dillian Whyte's message is 'we're standing by, we're ready' and Joseph Parker looks like a guy who doesn't mind who he fights."