The Korea Boxing Committee and a Korean promoter are in talks with the World Boxing Council (WBC).
"We expect that the bout, along with the World Cup, will attract tourists to Cheju Island and boost its image," a Cheju sports official said.
Cheju joins Bucharest, Indonesia, California, Texas, Michigan, Georgia, England, Denmark and the Netherlands, the Phillipines, South Africa, and the Lebanon as possible venues for the fight.
The WBC will select a host later this week for the fight, expected be held around 9 June
