Despite being past their peak, two-time world champions Joshua, 36, and Fury, 37, remain two of British boxing’s biggest crossover stars of their era.
The super-fight has been orchestrated by Alalshikh, with Joshua and Fury’s teams dealing directly with the Saudis over their contracts.
Hearn says neither Matchroom nor Warren’s Queensberry can act as lead promoter because it would give one fighter’s side an advantage over the other.
UFC chief White, the president of Zuffa Boxing, has said he is central to staging the fight, saying he knows the date, location and that he would promote it.
Fury was present at the UFC’s White House show on 14 June and teased a “massive announcement” from White before revealing he would be promoted by Alalshikh. Warren later told BBC Sport that Queensberry would continue to promote Fury alongside Alalshikh.
“The contract clearly states that Dana White and Zuffa Boxing, or anyone associated, cannot be the promoters of this event,” Hearn said.
“The only way Dana could have any involvement in the show is if we let him. And it’s not really how I’m feeling at the moment.”
Hearn believes White’s comments stemmed from Alalshikh asking him to explore the financial viability of staging the fight in Las Vegas, and that the UFC president then overstated his role in the event.
Asked if he could change his stance on White’s involvement, Hearn added: “Money changes a lot of things.”
Hearn and White have also built up a public rivalry since Zuffa Boxing entered the sport. White has signed Conor Benn, who was previously promoted by Matchroom.
Alalshikh has suggested next week’s meeting will include peace talks between the two, but Hearn feels his rivalry with White is “the best thing” that has happened in his career as a promoter.
“I would be disappointed if Turki Alalshikh makes us find peace, because I want war,” he added.
