Joshua's promoter Eddie Hearn will probably watch the proceedings in Auckland – Parker and his team today released a video featuring several of Joshua's falls, including his hitting the canvas halfway through his epic fight with Wladimir Klitschko at Wembley in April - with an air of bemusement.
Higgins said if anyone in the United Kingdom could find evidence of Parker being similarly hurt he would pay them £10,000 (about $NZ20,000), and Kiwi Parker pledged to match it.
No fighter has gone on the offensive to this extent before fighting Joshua and certainly none have before the fight has even been agreed.
Negotiations are continuing between Hearn and Higgins, with emails going back and forth, and needless to say this latest announcement will attract Hearn's attention.
Figures haven't been mentioned, but Higgins has now insisted he won't agree to anything less than 35 per cent of the profits the fight would generate.
That's down from 40 per cent but it would still be a very large figure indeed – many millions of dollars.
It will come down to money, of course it will, because it's professional boxing.
Higgins said Joshua and Hearn had no excuse not to agree to the deal because the 28-year-old Joshua has continually said he wants to unite the world titles, and claiming Parker's WBO belt would be another step on the way.
"They've said, loudly, that they want to unify and they can't unify without us unless they want to break their word," Higgins said.
But Higgins' firm line on the money is the one big excuse that Hearn and Joshua will cling to should they not want to risk it all.
The pair will likely say that Parker has no rights to such a big pay-day given Joshua is the one with the profile and pulling power, and negotiations will continue or stop.
Parker has a ready-made alternative in Australian Lucas Browne, also undefeated.
A contract has been signed with the contingency that a Joshua fight would take precedence in which case Browne would be paid a sum of money for his troubles.
A fight between the pair would be a good transtasman scrap but wouldn't make Parker anything like what he could earn fighting Joshua.
It is a risk and reward scenario and both are substantial as far as Joshua is concerned.
As for Joshua's chin - it truly doesn't appear to be as good as Parker's and for all the Englishman's physical advantages, this is one area where he might fall short.
Time will tell and hopefully sooner rather than later.