"He's treating it as not much better than a voluntary defence rather than as a unification bout, and Joseph is a world champion in his own right," he said.
"Ringing him and pandering to him isn't going to improve the deal. There's nothing really to say at the moment. The ball's in his court.
"Look, this fight will happen eventually - history has shown that these fights are made when they are closer to 50-50 or even 60-40. Eddie should fast forward that process and do a fair deal now. It's up to him."
Hearn is also negotiating a deal to fight American Deontay Wilder, the other recognised world champion in the division, and in Parker's favour is the fact that Hearn is likely to want Joshua to fight the 25-year-old New Zealander before the hard-hitting but flawed Wilder.
Joshua is on holiday in Dubai after his recent victory over Carlos Takam, and the British boxing public are likely to demand a unification fight next. That could happen in March or April, with Australian Lucas Browne primed as a back-up opponent for Parker should the Joshua fight not get made.
Higgins said Parker would be happy to fight Wilder instead should Hearn refuse to budge in his twin-negotiations.
To his credit, Joshua has appeared genuine when saying he wants to fight Parker and Wilder next year, and in an interview in Dubai he refused to downplay a potential challenge from Parker.
Asked if the Kiwi would be a "stepping stone", Joshua replied: "Never a stepping stone. They're all challengers. They could all be my last fight [as champion]. I have to look at it as a challenger, that's my mindset.
"I can't look at Parker, I can't look at the up-and-coming heavyweight, as a stepping stone. In the heavyweight division, one mistake and it's like snakes and ladders - you go back down. Parker is definitely a real challenge."
