Schmeichel has made over 300 appearances for Leicester since they signed him from Leeds in 2011, and he was ever-present when they sensationally won the Premier League in 2015/16.
But there are murmurings of discontent at the King Power Stadium, with some players - notably star striker Jamie Vardy - known to be sceptical of Puels tactics.
Peter Schmeichel appears to have the same doubts about Puel as he claimed Leicester, who are currently 12th, should be challenging for a place in the Europa League.
"Leicester City are a really good football club," he told BeIN Sports, quoted by the Leicester Mercury.
"They’ve got good players, they just don’t have the manager who can get the best out of them.
"Once they get everything sorted out - and I leave it to you to interpret what that means - you’ll see Leicester maybe in fifth to eighth place where they belong."
Schmeichel has been linked with clubs like Chelsea and Roma in the past. Asked whether his son would consider leaving Leicester, Peter Schmeichel said: "Of course he wants to challenge himself like any other player.
"But I don’t think he wants to go to Europe. I think he loves England too much, I think he likes the Premier League too much, so it’s a difficult one."
Schmeichel signed a new contract last summer tying him to Leicester until 2023, but at the age of 32 he may feel that now is he time to broaden his horizons.