The Foxes turned to former Southampton manager Puel in October after sacking Craig Shakespeare, and the decision seemed bizarre given his less-than-impressive season with the Saints.
However, Puel won five of his first eight games in charge, losing just once in a start which silenced his doubters – but recent form has seen them return, with only two wins in 11 games.
Saturday's 5-0 defeat at Crystal Palace has sparked questions over Puel's future, and the Daily Mail report that Leicester may decide to move on from the 56-year-old.
It's claimed that Marco Silva – sacked by Watford in January despite a strong start to the season – is being lined up by the Foxes as a replacement, in a move which could frustrate Everton.
The Toffees pursued Silva as Ronald Koeman's successor in October and November, with Watford standing firm before sacking the 40-year-old just months later, and he appears to still be on Everton's radar.
The Mirror claim that Everton want either Paulo Fonseca or Silva to replace Sam Allardyce this summer, but with Fonseca looking unlikely and Silva now potentially heading to Leicester, majority shareholder Farhad Moshiri could see his top two targets slip away.
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