The Mirror says Leicester had made a £3million bid for Naughton, who had previously enjoyed a successful loan with the Foxes.
But Swansea is believed to be the player's preferred destination and the clubs are expected to agree a deal worth around £4m, as the Welsh club spend a slice of the £30m sale of Wilfried Bony to Manchester City.
Naughton, 26, has fallen down the pecking order at White Hart and is keen to play regular Premier League football.
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