"We're looking at fighting in March or April. If they're keen to fight (then), we're very keen to fight. It's time that all the heavyweight champions unified so we can see who the best in the world is.
"That's the reason why we're trying to chase this."
He added: "There is no real timeframe. We're open to suggestions from their side. We have a date we want to fight on but they might have a different date so it's about finding some common ground and meeting in the middle."
Parker has been out of the ring since his victory over Britain's Hughie Fury in September. Joshua, meanwhile, is being lined up for a trilogy of heavyweight mega-fights, with Hearn hoping to make fights with WBC champion Deontay Wilder, Parker and ex-unified king Tyson Fury to crown an undisputed king of the division.
The WBO champion is confident his and AJ's team can settle their contractual differences and begin a potentially historic series of unification bouts. But the New Zealand fighter claims he is prepared to forgo his "preferred option" if terms cannot be agreed.
"If it was about the money, I wouldn't have been calling out AJ two years ago or a year ago. I was calling him out and wanted to fight him then, even at that stage, even when it wasn't worth a lot of money," he said.
"But I've always wanted to test myself, I don't mind fighting Wilder - if his team came and said 'we have a good offer for you' and it was a good offer that we're all happy with then maybe we'll go down that route," he added.
"I just want to fight the best out there and I think, respectfully, AJ is one of the best and Wilder is one of the best because they're both champions. So I'd like to test myself against the best champions... (but) there is Tony Bellew, Lucas Browne, there are a lot of options there.
"The thing about the heavyweight division now is that it's exciting because there are so many options and I don't really care who I fight, I just want to fight whoever is keen to fight."
Joshua, however, remains the New Zealander's No 1 target. Though he believes their unification showdown could grow to become even bigger down the line, the unbeaten heavyweight has urged his British rival not to "miss out on the opportunity of two good champions fighting".
Since their respective victories over Carlos Takam and Bermane Stiverne, however, talk of a clash between Joshua and Wilder has gathered pace.
Parker believes he is being both "overlooked" and "underestimated", something the 25-year-old, who is unbeaten in 24 professional fights, believes AJ would be doing at his peril.
"It's a good fight, we're both going to throw a lot of punches, a lot of bombs. I back myself and I feel I can knock him out," he said.
"I feel I have a good chin and he has been dropped a few times. I'm not saying he's not a good fighter but he's been dropped so I think there is a bit of weakness I can get on top of and I feel like I can KO him."