The reigning Premier League champions offered £12m for the centre-back in their third bid, but even that sum was apparently not enough to convince the Serie A club to sell.
Leicester will however not stop looking to bolster their defence, they will just turn their attention to other targets.
Schalke centre-back Matija Nastasic, who had a spell at Manchester City after Fiorentina, is reportedly to the liking of Claudio Ranieri, though he is recovering from a groin injury.