Money is the issue of course. Hearn denies offering Parker 20 per cent of a Joshua purse, but there is little doubt he is trying to lowball him, and in the meantime Higgins is lining up one or two voluntary defences in order to provide lucrative options for his man.
Higgins said today that he was doing "due diligence" on a "reasonable option" for Parker's next opponent, and that an announcement is imminent.
The major problem with Parker's position is that his profile is far lower than that of Joshua and Wilder, the WBC champion, and therefore any fight he is involved in will in theory generate less revenue.
Wilder's promoter Lou DiBella said: "Joe Parker - is that a defining fight? I don't know [but] it is a unification fight. But really, the fight that turns Deontay Wilder into the kind of star that he wants to be is Anthony Joshua."
Parker wants to fight either man and believes he has the tools to beat them. Certainly, his reputation should have been boosted after Carlos Takam, a man he beat by decision last year, recently took Joshua 10 rounds despite having little time to prepare, and there is no doubt Parker would put pressure on Wilder (the only way to beat him).
Joshua looked big and slow against Takam before stopping him in Cardiff with the help of referee Phil Edwards and while Wilder looked extremely impressive against Stiverne - winning with a first-round knockout - his Haiti-born opponent appeared catatonic on his way to the ring, a state he remained in once the first bell rang.
Wilder's jab found its mark from the start, but his best punch of the night was his straight right hand which put Stiverne on his back the first time.
Wilder v Joshua is the heavyweight fight the boxing world wants to see, and that demand could force Hearn and Joshua to do business with DiBella and Wilder, and the American's manager Al Haymon.
If not, Parker is poised to take advantage, but even as the owner of one of the four recognised world heavyweight belts, getting Hearn or DiBella to the negotiating table, and then making a deal, will not be straightforward.