The pair have been instrumental in the club's rise to the top of the Premier League.
Given the time left to run on both of their contracts - The Sun reports that the right-back's deal expires in just over a year, while Schmeichel signed a new four-year contract in 2014 - getting either tied down may not be considered urgent, which suggests that both are being rewarded for their part in the Foxes' amazing season.
The Dane - who has attracted interest from Manchester United and Tottenham (via The Sun) - has started every single game for Claudio Ranieri's side this term, and has pulled off some stunning saves, including a brilliant reaction stop from Fernando during the 3-1 victory away at Manchester City.
At the time, the score was 2-0 to Leicester with around 35 minutes to go, so a goal at that point would have changed the complexion of the game immensely.
Similarly, Simpson has been an important member of the side, making 18 appearances in the top flight. Along with Wes Morgan, Robert Huth and Christian Fuchs, the pair have formed part of a solid back five that even Ranieri has struggled to find reason to tinker with this season.
And if they can join Jamie Vardy in committing their future to the club (via The Sun), then it will undoubtedly provide the team with the kind of boost they need if they are to remain at the top of the table until the end of the campaign.