"The only bigger purse has been when Parker fought Andy Ruiz Jr and won the world title. Junior Fa was offered the second biggest purse ever to fight the guy he had been calling out for two years. We can't get a response.
"The only explanation is Junior Fa is using Joseph Parker to build his name and then he's offered $500,000, enough to buy a house, and he runs."
Parker, who is keen to get back in the ring this year against his old amateur rival, is desperate to work his way back towards a world title shot, while Fa is also looking to make his mark on the heavyweight division.
The former WBO champion Parker (27-2) is currently ranked No 2 in that organisation, No 7 with the IBF and No 6 with the WBA, and has is on a three fight winning streak after losing his belt in 2018.
Fa has risen to No 6 with the WBO and also sits at No 14 with the IBF after racking up an unbeaten 19-0 record.
Fa's American promoter Lou Dibella, who also works with Deontay Wilder, hit back at Higgins saying the offer was "unacceptable".
"I found the offer, guarantee and upside, to be totally unacceptable for one of the biggest fights in New Zealand boxing history," he told Sky Sports UK. "I didn't accept it. I will be discussing it further with Junior's team shortly.
"Under Higgins' offer, the fight would need to do huge business for the Fa side to see NZ$500,000 between us. They can't assert how big the fight is and act like Junior is an insignificant participant."
Higgins wants to try and flush out Fa by taking the negotiations to the media, further annoying DiBella.
"Here are the facts. Junior Fa, who has fought no-one, has been calling Joseph Parker's name through the media for two years to build his name in New Zealand," Higgins said. "The Parker-Fa fight has meaning in New Zealand, but not really outside. If DiBella thinks otherwise, I invite him to put an offer on the table for international television rights. He won't.
"It's a bad look if they don't take the fight, so that's why they don't like it in the media. Long story short, if they believe Junior Fa would win the fight, they wouldn't have a problem.
"Joseph Parker is the A-side, he should be paid triple Junior Fa, but he is willing to fight Junior Fa for the same money. They are running scared is what's going on."
UK promoter Hearn is reportedly eager to launch streaming giant DAZN in New Zealand, and an all-Kiwi super fight featuring Parker and Fa would be the ideal bout to debut the streaming service.
Parker and Fa currently sit on two wins each in their amateur fights against each other.
