Schmeichel, 27, is out of contract at the King Power Stadium at the end of the season and has reportedly attracted a lot of interest.
Milan are one of the clubs to have been linked with the goalkeeper, and are now thought to have made an approach to the Foxes.
The Italian side have previously been connected with Newcastle United's Tim Krul as they try to bring in a new keeper.
Schmeichel's Leicester team-mates Moore and Schlupp have also been the subject of speculation during the transfer window, and it is understood by Sky Sports that Fulham are keen on both players.
The Cottagers are believed to have made a fresh bid for defender Moore and also made an offer for versatile 21-year-old Schlupp.
Fulham are in the market for new signings as they battle to avoid relegation from the Premier League.