The centre-forward has announced in the Algerian press he wants to leave the Foxes in January.
Palace are keen, where Slimani would arrive as competition for injury-plagued centre-forward Christian Benteke. However, Palace are not alone in their interest.
Also keen are Rennes, which are interested in taking Slimani on-loan for the second-half of the season.
Slimani is in his second season at Leicester after joining last year from Sporting CP.