The centre-back was signed by City in 2011, having come through the Feyenoord youth academy in his native Netherlands, and the former Arsenal legend is not shy of imposing some lofty expectations on the 17-year-old.
"Karim has the natural air of a central defender," Vieira told De Telegraaf. "This boy has so much talent, if he doesn't make it, it will be a big failure for us.
"Of course we put a lot of pressure on ourselves but Karim also knows he has the responsibility to make it to the top. He looks older and he also made his debut in Mancini's first team, but he still is only 17. He's one of the best in our academy."
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"Last year I was at Feyenoord v Ajax," said the Premier League great. "There were a lot of young talents on the pitch and I thought Feyenoord were great - Ajax weren't so good. But a year later they beat us in the Champions League.
"That's why we also need to go in that direction. A clear philosophy around the whole club."
Rekik himself has also spoken of his future at Manchester City, insisting that he has no regrets about joining a club where competition for senior places is perhaps more intense than at Feyenoord.
"Of course it's great that guys from my youth teams like Tonny Vilhena and Jean-Paul Boetius play in the first team at Feyenoord," he observed, "but I chose for this path to reach the top.
"I want to become one of the best defenders in the world and I can train with the best players at City.
"At Feyenoord I won in the youth because of my physique, but when I play [Mario] Balotelli or [Edin] Dzeko, [physique] is not enough. Every day I get tested."