The 27-year-old's contract with the promoted Championship outfit expires this summer, three years after he joined from Leeds United.
An ever-present for Leicester during their league campaign this season, Schmeichel has been linked with a number of clubs including AC Milan and was awarded his third international cap for Denmark in last month's friendly against England.
"I have never hidden how much I enjoy to play for Leicester," he told Danish television channel TV3.
"It is a fantastic club, where I have been happy from the first day. I can just sit and wait for the club right now, there is nothing else I can do at the moment."
Meanwhile, Leicester striker Marko Futacs, currently on loan with Diosgyor in his native Hungary, has eyes on returning to the King Power Stadium for a taste of Premier League football next season.
The 24-year-old, who has 15 caps for his country, made a handful of appearances mostly as a substitute for Leicester in 2012/13 but has since spent time with Blackpool as well as Diosgyor.
"Of course it would be great to play against Chelsea, Manchester United, Arsenal or Liverpool," the former Portsmouth player told Nemzeti Sport.
"I'll see what their plan for me is (at Leicester). But I won't panic if I have to continue my career at home. I have to play well to be called up by the national coach for the European qualifiers."