The 26-year-old, who helped Italy reach the Euro 2020 final, had an impressive 2020-21 season for his Serie A club, scoring 17 goals and providing eight assists in 30 league games.
Berardi still has three years to go on his contract but there have been suggestions that he could continue during the transfer window this summer.
According to La Stampa, Liverpool are “targeting” the Italian international, the “tempted” to look for new ways in the current market.
The report claims the Reds are considering an offer of 40 million euros (£ 34 million), although each move may depend on Mohamed Salah leaves before the new season.
Berardi, who Liverpool sees as a potential alternative to PSV Eindhoven’s Donyell Malen, has scored 105 goals and provided 67 assists in 291 games for Sassuolo.