A fight to unify Joshua's IBF and WBA world titles and Parker's WBO belt would probably happen in March if it is made.
Parker's team went from 40 per cent of the profits to 35 per cent and are refusing to budge from that figure.
Higgins yesterday said Joshua was "driven by fear and greed".
"He is scared that Joseph Parker will break his glass jaw ... that's the fear," he told British blogger PSB Sports. "And he wants a bigger percentage of the pie that is fair, and that's the greed kicking in.
"So Anthony Joshua's fear and greed are what's stopping the unification happening."
Higgins said Joshua had "drawn a line in the sand and won't move" in terms of the money split for the fight.
Higgins has called the negotiations "a stalemate", but Barry was more positive.
"We're waiting on Anthony Joshua to make a small concession on a couple of points and the fight will be done," Barry said.
"Eddie wants the fight, there is no doubt about that. Sky UK want the fight. The boxing world wants this fight and the heavyweight division needs this fight."