Lupesoliai La’auliolemalietoa, 33, lost his WBO world championship to AJ, 35, in 2018, and Parker is now looking for revenge.
Speaking with Sky Sports, he said: “I've been wanting a rematch with Joshua. I want to avenge those losses.
“I know AJ's another big fight, I don't really care who I fight, just make sure it's someone who's top five in the world.”
Parker added holding the WBO title was a “bargaining chip” for potential future fights.
He said: “It's a bargaining chip, being the champion of the world.
“You want to win it so it would be nice to fight someone to win it. I know you can get elevated to it and it gives you a bit more bargaining power. But it would be nice to fight for it.”
Even so, Parker said he had “unfinished business” with Daniel Dubois, 28, who pulled out of their IBF bout in February due to illness.
He said: “There is unfinished business and if he wants to get it on we definitely can.
“There's no point avoiding fights. Whatever they put in front of me, I'll take. Obviously I'm very close now to fighting for the championship of the world but I just don't want to wait around.
“That's another way of getting closer to the championship of the world - beating whoever's in front of me.”
Parker is due to face Fabio Wardley, 30, next month in London, and the WBO have ruled that the winner of that match will be the mandatory challenger to reigning champion Oleksandr Usyk, 38.
Parker said: “They're saying the winner of this fight gets Usyk next. They can say whatever they want to say, but Usyk holds the decision who he wants to fight.
“That fight's there but it's whoever Usyk wants to fight. For now I'm just going to fight who's in front of me and just enjoy it all.”
Reflecting on the possibility of fighting The Cat - who has defeated AJ, Dubois, and Tyson Fury, 37 - Parker insisted he could “show something different” to Usyk’s previous victims.
He said: “If that opportunity came I feel like I can show something different. Experience, skill, belief, power, speed, movement, I feel like I'm getting better and better as a fighter even though now I'm 12 years in the game.
“I know what I can do. I back myself and believe in what I can do. But that'll be there once I do this fight.”
