Russian Bivol avenged a previous defeat to take the undisputed light-heavyweight world title from Russian-born Canadian Beterbiev, who had won the first fight in October.
This time, Bivol won an epic rematch on a majority points decision after the judges scored the fight in Riyadh 114-114, 116-112 and 115-113.
"I think we need the third fight between Artur and Dmitry, as we have just witnessed no less than the event of the year, and we need to repeat it," Kremlev said.
"These guys are truly the best boxers in the weight division. Whatever the cost, we will bring this fight to Moscow, and we are starting the negotiations.
"I envision it at Luzhniki stadium with nearly 100,000 people (in the) crowd."
Beterbiev had said he did not want a second fight but vowed to make a comeback for the third, while Bivol said he was up for any challenge if they were to fight again.