Main Events CEO Kathy Duva, who promotes Kovalev, informed the World Boxing Council this week she will not participate in a purse bid scheduled for Friday in Mexico City.
Kovalev is under contract to the HBO specialty channel, while Stevenson is managed by Al Haymon, who stages fights on rival Showtime or on the Premier Boxing Champions series on CBS, NBC or ESPN.
Duva said in a letter to the WBC that, if she loses the purse bid, Kovalev could not fight on another network. She also said that the bout won't happen until the fall and it is too early to set the purse because economic conditions may change by then.
Stevenson's promoter Yvon Michel answered Wednesday with a letter to Duva, also sent to the media, asking her to let Kovalev have this one fight on another network
Michel said it is important to maximize revenue from what should be one of the biggest bouts of the year.
"If you do not believe the potential economic success of this event, or you are concerned of not receiving the necessary backing, just sit back and let us take the risk and do the job," said Michel. "Your fighter will make as much money in this single fight than all his other career fights combined.
"We believe the Stevenson vs. Kovalev light heavyweight unification title fight is the most anticipated and publicly demanded fight of 2015, ranking only behind Mayweather/Pacquiao. We also believe it is one of the most important fights in the history of the light heavyweight division."
He added that his promotion company Groupe Yvon Michel is "willing to accept your offer of co-promoting the fight together with a 50-50 split and avoid going to purse bid.
"However, one major point is we have to be able to maximize revenues in all departments, including television. We cannot blindly agree to a deal. We need to know how much HBO is willing to invest in a licensing fee, in comparison to what we can get on our side, in order to choose the best offer.
"You have very often publicly stated Stevenson was an ordinary fighter ready to get beat. If it is the case, there is no risk for you. You win and bring Kovalev back on HBO right after."
Kovalev, coming off a decisive win in March over Jean Pascal in Montreal, holds the WBA, WBO and IBF light heavyweight belts, while Stevenson has the WBC title. Both hope to unify the titles from the four main fight sanctioning bodies.
But both plan to fight again this summer before they face each other. Kovalev wants to make a mandatory defence against Nadjib Momammedi to ensure he keeps his IBF belt. Stevenson's next opponent is yet to be determined.
It was Duva who had asked the WBC to take the unprecedented step of ranking a champion from other sanctioning bodies as mandatory challenger in order to force Stevenson to accept a fight with Kovalev. She had earlier accused Stevenson of ducking difficult opponents.
Duva's letter to the WBC included more jabs at Stevenson, suggesting that his popularity was in decline both at the gate and on TV. Michel said ratings from Stevenson's recent win over Sakio Bika showed otherwise.
More verbal sparring is likely before a deal is set.