"My gut tells me it's 50-50. Our team really wants it. We're 100 per cent in the fight. On their side, I'm not so sure. There's a lot of talk there and it's hard to gauge. I think for Joshua and their team it shouldn't be about the money it should be about his legacy and trying to unify the belts and seeing who the best is.
"They can easily take a voluntary and make big money but for us I think they should pay us a bit more because I have a belt."
Parker's back-up option is undefeated Australian Lucas Browne, a fight which has merit too for the transtasman aspect and the fact Browne has punching power and an aggressive attitude in the ring.
But Browne, who has already agreed terms, could easily be an opponent later next year too. For Parker, who has watched with interest the rivalry building between WBC world champion Deontay Wilder and Joshua, the IBF and WBA title holder, it is a case of taking his shot while he can.
Should the Parker v Joshua fight not get made, a Joshua v Wilder bout, which would attract interest worldwide and particularly on both sides of the Atlantic, could easily lead to one or more re-matches and Parker could be left out in the cold.
"I'm not scared of anyone," Parker said. "They may be big giants, and I respect Wilder's power, but I think they're both beatable.
"Everyone wants to know who the best is. I want to know who the best is - that's why I want to fight these guys."
Should he fight Browne instead - a bout which would probably be held in Sydney or Melbourne - a decent scrap would be the result. In a reference to the evasive Hughie Fury, whom Parker beat on points in Manchester in September, he said: "I like people who stand there and fight - not people who put on sneakers and run around the ring."