Parker, the WBO champion, and Joshua, the IBF and WBA champion, both want the fight to happen and it seems there is finally some movement in the stalled money talks to increase the possibility of a showdown in the ring next year.
"We weren't happy with their starting point but they have signalled they are willing to move a bit. We are in the middle of that negotiation now," Duco Events boss David Higgins said on Thursday after a night of productive talks with Joshua's promoter Eddie Hearn.
"We know exactly what the lines are, both parties want the fight but we have to settle on a fair deal."
Higgins said they didn't want to be handed a fixed fee for the fight.
"We want utter transparency ... open books, all the revenue in the pot and all the costs, a right of audit and then a share that we feel reflects Joseph's status as an unbeaten champion as a ratio of the overall pie," Higgins said, conceding Joshua deserved more.
It's now just a matter of how much more.
While figures remain private while negotiations continue, Hearn has signalled Parker's value at around 20 per cent of the purse while Higgins wants 40 per cent for his fighter. Finding the middle ground finally seems to be happening.
Higgins and Hearn are no strangers and this is their personal duel - a fight to set up the real fight.
"Eddie is fairly straight forward and he's professional. He's just trying to drive a hard bargain," Higgins told Stuff.
"In driving the hard bargain though, we urge him to consider that Parker has come from the ground up, he's earned that title and in unifying he is putting that all on the line.
"He has a large extended family to look after. Joshua has had the privilege of setting himself and his family up for life and for us, it's a bigger deal than for them. For AJ, maybe the money might be a bit of a drop in the ocean. For us, it makes a meaningful difference to four or five years of very hard work and risk by Joseph, Duco, Kevin Barry ... the whole team.
"When we started this, it was 'let's try and do the impossible'. Having got there and then being willing to unify ... unifications only happen once or twice in a decade ... that deserves a fair deal."
Higgins said they wouldn't be rushed into anything and there was no timeline to get the fight signed off.
He felt Parker was in a powerful position in having decent alternatives, including a possible crack at the other unification fight in the mix against WBC champion Deontay Wilder. Potentially lucrative fights in Australia, China, Russia and the United States were also in the mix. Higgins has also raised the possibility of fighting Tyson Fury if the former champ can get his game together again.
"It's a moving feast, a deal will be done when both parties are happy with the deal," Higgins emphasised as talks with Hearn were set to resume on Thursday night.
"Again, if they don't get close to where we want to be, we are Ok with fighting Wilder or whoever and then we will come back to it later.
"But if we can get close, then it's on. Joseph wants to fight Joshua."
The Joshua camp are also trying to sort out a unification fight with Wilder as they map out what could be a huge 2018 for the glamour division.
As the debate rages over who would be the more meaningful opponent for Joshua, legendary ring announcer Michael BUffer, the man who coined the phrase "let's get ready to rumble", put his voice in for Parker.
Buffer felt Joshua v Parker would be "a better match than many say. Joe is underestimated, he can bang", and urged the promoters to get the deal done, saying "unification is what we all want".
Photo by: PHOTOSPORT. Caption: WBO champion Joseph Parker is eager to fight Anthony Joshua and his promoter David Higgins is desperately trying to make that happen.