The 26-year-old has two assists in three appearances at UEFA Euro 2020 and has attracted interest from the Rossoneri and the Foxes, according to Il Corriere dello Sport.
Although there are still no official offers on the table, both clubs have reportedly begun preliminary talks with Sassuolo.
Berardi’s contract at the Mapei Stadium expires in June 2024.
The Italy international is a product of the club’s academy and made his senior debut in a Coppa Italia tie against Avellino in 2012.
He has 105 goals in 291 appearances with the Neroverdi.
La Gazzetta dello Sport reported last week that both Liverpool and Tottenham are interested in the Italy international and Il Corriere dello Sport confirms more Serie A and Premier League clubs have set their sights on the 26-year-old.