Promoter Eddie Hearn says Anthony Joshua and Tyson Fury may consider dropping all four world title belts to ensure their potential fight happens.
The all-British heavyweight showdown would be the first fight in history in which all four heavyweight titles are on the line.
Fury, 32, is WBC champion while Joshua, 31, holds the IBF, WBA and WBO belts.
“We have a fight on our hands, and sorry to the governing bodies, that eclipses all belts,” Hearn said.
The promoter told Matchroom Boxing: “We’ve just got to be a bit careful because you may be on the verge of saying, ‘Let’s just get rid of politics right now. Let’s just drop all the belts because if we lose one belt, we might as well lose them all.’
“You’ve got the biggest fight in world boxing,” added Joshua’s promoter.
Joshua raised the prospect of a bout against Fury by knocking out Kubrat Pulev on Saturday.
But the WBO expects Joshua to face Oleksandr Usyk next, increasing the chance Joshua will give up the belt or Usyk will be paid to ‘step aside’.
Boxing’s governing bodies receive financial sums for their involvement in fights.
“You are paying each governing body hundreds of thousands of dollars,” Hearn continued. “Now you have got another guy who probably wants seven figures to step aside.
“We have just got to be careful because ultimately the aim of this fight has always been to be for the undisputed championship.
“We will do whatever we can to make sure that every belt in boxing is on the line in the Tyson Fury fight.
“What we won’t be is held to ransom and we won’t let politics get involved in a fight that boxing needs.”
On Tuesday, Fury’s promoter Frank Warren said the only thing that could prevent the fight was “egos”.
Warren pledged to work “collectively” to deliver the fight that he believes “all sports fans want to see”.
‘The fight to make the fight’ – analysis
BBC Sport boxing reporter Luke Reddy
Hearn appears to be applying some pressure.
WBO president Paco Valcarel tweeted soon after Joshua had beaten Pulev on Saturday to state Hearn “knows the meaning of commitment”.
It seems the sanctioning body is adamant its mandatory challenger Usyk must now have a shot at the title, regardless of the showpiece Joshua and Fury can put on.
This is the kind of issue that arises in a sport with numerous sanctioning bodies and vested interests. The politics create clashes, frustrations and – on times – road blocks.
Hearn’s stance seems to be to start a game of who blinks first.
Given Joshua and Fury can compete in an all-British affair, as the two leading heavyweights in world boxing, it’s fair to say the average punter on the street won’t care what belts or baubles are attached, so why are they needed?
The touch of history that having all four up for grabs will offer is however a seriously good selling point. And you can rest assured that deep down both fighters will not want to give up titles they worked hard to win in the first place.
As I wrote hours after Joshua’s win over Pulev, there are hurdles to overcome. Already we are seeing that the fight to make the fight is under way.