"Leonardo's contribution to the club has been a significant one and he will remain a popular figure among players, staff and supporters alike," Leicester said in a statement.
Algerian international Slimani struggled to nail down a starting spot since joining from Portuguese side Sporting in 2016 and was loaned to Newcastle United last season.
Fenerbahce, who were runners-up to Galatasaray in the Turkish Super Lig last season, kicked off their campaign with a 2-1 win at home to Bursaspor on Saturday.
Leicester, who lost 2-1 to Manchester United in their season opener on Friday, host Wolverhampton Wanderers next weekend.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge and Pritha Sarkar)
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