Higgins told Omnisport: "We are not in a hurry, because for us there is a dignity about it. We want the fight, we will take it next, but we will not do it if we don't feel we are being treated reasonably.
"We think we win the fight as Parker has never been [knocked] down, he has a rock-solid chin and AJ has been down more than once. At best it's a 50-50 fight, but we think we win.
"That could be why they are dragging things out. Anyone who thinks Joshua walks through Parker is dreaming."
Higgins believes it is only matter of time before the fight happens, but an agreement will only be reached if the Joshua camp show some respect.
"A mandatory pays about 30 percent generally, we know that Charles Martin was paid more than $5 million and we think [Kubrat] Pulev was around that. I won't disclose what we've been offered, but it's a lot less, so we think it's not a fair offer," he said.
"I think they are trying it on, because they probably think we are from New Zealand, we are not as experienced, not used to the big time, that type of assumption. They will find out that is not correct."
Higgins added: "I think the fight has to happen.
It would be embarrassing for AJ to proclaim he wants unification, then not make a deal with [Deontay] Wilder or Parker. I'm sure AJ and Hearn have enough money for life, so it's about legacy and unification.
"They have said that, so they have just got to get closer to a fair deal and we are on. We don't care where or when, we will fight him anywhere.
"These big fights always happen, whether they happen quick or slow is down to greed and realism."