The Foxes need to beat Nottingham Forest at the weekend to stand a chance of making the playoffs, with Schmeichel 'desperate' to play at the highest level.
"It is a short career and I have ambitions to play in the Premier League. There is no doubt about that," Schmeichel told reporters at a press conference.
"I am incredibly happy at Leicester and I would like to be in the Premier League with them. That's my ambition."
The 26-year-old, who is the son of former Manchester United goalkeeper Peter Schmeichel, has been linked with a host of Premier League clubs following his performances this season.