Leicester had two bids for Michael Keane turned down by Burnley and will reportedly not come back with a another offer for him as they are looking to add some depth in the defence.
Manager Claudio Ranieri has therefore turned his sights to his compatriot Acerbi, who turns 29 in February.
The Italian defender, who had joined Sassuolo four seasons ago, underwent treatment for testicular cancer in 2014.