The 76-year-old, England's goalkeeper when they won the World Cup on home soil in 1966, believes promoted City will find life difficult as they return to the top flight for the first time in a decade.
"It is really tough in that league and it is a totally different game," Banks told the Leicester Mercury.
"It is a really big step up ... I hope they stay up but I wouldn't put money on it."
Banks, however, said he had been impressed with Leicester goalkeeper Kasper Schmeichel, son of former Denmark and Manchester United F.C. great Peter.
"I've been to watch him play quite a bit," he added. "I've liked what I've seen, he looks the part.
"I'm surprised no one has been in and grabbed him, especially the top Premier League teams, but I think it might be a bit too much if they have to rely too much on him."
Schmeichel, who joined Leicester from Leeds in 2011, says he is proud of the honours his father won. Peter landed a string of trophies with United including the Premier League-Champions League-FA Cup treble in 1999.
"My dad had a great career and if I could win a 10th of what he won in football I'd be happy," said the 27-year-old.