Vieira, the 1998 World Cup winner who managed Olise during his time at Crystal Palace, made the comparison in an interview with L'Equipe.
"It's the future that will tell us if he's a Zidane, if he's a Platini, if he's a player of that level. But there's one thing I'm convinced of: he has the potential. He has Zidane-like potential. He has that creativity, that finesse, that creativity, that efficiency," Vieira said.
"What he did with Bayern this season is already pretty extraordinary."
Vieira believes Olise's best years are still ahead of him as he gains further experience for both club and country.
"He's a player who, with experience at club level and with the France national team, is going to gain maturity. And with that, he's someone who is going to explode. He's a future Ballon d'Or, simply put," Vieira said.
"The World Cup will give him extra confidence, and after that, he'll completely explode in the eyes of the world."
Olise has emerged as one of the standout performers in European football over the past year, with his form for Bayern Munich drawing interest from Real Madrid, even as the Bavarian club insist he remains firmly off the market.
Vieira's endorsement carries particular weight given his own playing career and his direct working relationship with Olise during the winger's formative years in English football, before his move to Germany transformed his profile on the continental stage.
Olise joined Crystal Palace from Reading in 2021 and spent three seasons under Vieira's management before later coaches at the club, before his eventual move to Bayern in 2024 took his career to an entirely different level.
His performances since have established him as one of the most sought-after attacking players in world football, with his World Cup involvement this summer offering another platform to enhance that reputation further.