According to SkyBet, Kim and Moon's win coefficient is 4/7, which means that the odds of their victory stand at 63.6 percent.
The forecasts from Ladbrokes and Coral gambling companies have shown that the two leaders are 60 percent and 54.4 percent likely to secure the prize, respectively.
Carles Puigdemont, the former Catalan president, is 5.9 percent likely to be awarded the peace prize, SkyBet said.
Russian President Vladimir Putin's chances of winning are estimated by the bookmakers at 3.8 percent.
The winner will be announced on Friday.
The situation on the Korean Peninsula started to de-escalate earlier this year, when Kim announced he was ready to denuclearize and make peace with South Korea. He and Moon have held three summits over the past eight months during which the two leaders agreed to settle the issues of separated Korean families, putting a formal end to the Korean War and building a lasting peace on the peninsula.