The commanding central defender enjoyed a successful loan spell with Sampdoria last season, having previously spent two seasons with Crotone. While at the Genovese club, the 26-year-old was called up by Italy for the friendlies against Argentina and England in March.
Everton lost Ramiro Funes Mori to Villarreal last month with the 27-year-old signing a four-year contract with the Spanish club.
West Ham landed Issa Diop in a £22m deal from Toulouse earlier this month but lost James Collins and Patrice Evra on free transfers, as well as youngster Rosaire Longelo.
The Hammers conceded 68 goals last term, which was the joint-worst in the Premier League. Everton, keen to push for European places, know that a repeat of the 59 goals in the ‘Against’ column must be avoided.
Despite signing for Sassuolo in 2016, Ferrari has yet to make a league appearance for the Neraverdi, repeating the pattern of his five-season stint with Parma after turning professional in 2009. Corriere dello Sport claims Sassuolo are open to selling the player if an acceptable offer is received.
The Premier League duo face competition from Spartak Moscow according to reports in Italy.