The former Stuttgart and Bayer Leverkusen coach believes the 21-year-old is destined to become one of the best in the world, despite an unspectacular start to life with Bayern
The Germany international is regarded as one of the biggest talents in Europe, but he has so far been unable to make an impact at the Allianz Arena, primarily because of injury.
Nevertheless, Daum has little doubt that Gotze will eventually prove a big success with the Champions League holders.
"Mario has extraordinary abilities. He will become another Messi. Bayern wouldn't have spent as much money on him if they didn't think he'd become a great player," the former Stuttgart and Bayer Leverkusen coach told Sport1.
"This is a transitional year for Mario. He has not reached the top step-by-step, but has developed incredibly fast in recent years. His progress has halted a bit now due to injury, but that's only normal.
"It's all about adapting this year and I can guarantee that next season will be his big break-through."