The 22-year-old has been vocal in his desire to test himself at the highest level again after briefly tasting Premier League action with Manchester City in 2007.
His hopes of achieving that dream with Leicester were dashed when the Foxes crashed out of the Championship play-offs to Watford last month.
That led to speculation the Denmark international could quit the King Power Stadium for a Premier League side, with Championship runners-up Hull City frequently mentioned.
Schmeichel's father Peter has revealed the Tigers have made two offers to land his son and are among a clutch of teams keen on signing him.
Schmeichel senior played alongside Hull boss Steve Bruce at Manchester United between 1991 and 1996 and believes his son would benefit from working under him at the KC Stadium.
"There are several interested clubs," Schmeichel told DR. "Hull made two official offers and they have a great manager, Steve Bruce, who is one of my best friends.
"Steve has known Kasper since he was three years old and Kasper and [Bruce's son] Alex grew up together, so that is a fantastic story.
"But how it all ends up is up to Kasper, his agent and the clubs. It is not easy because he is playing at a club that does not want to sell him."