The Spanish outlet claim that the Hammers will look to make a move for the Portuguese international should Declan Rice leave the club amid reported interest in the youngster.
Estadio Deportivo claim that the Premier League club attempted to sign the 27-year-old from Sporting Lisbon last season before missing out to the La Liga side.
Carvalho enjoyed a great year, winning the UEFA Nations League with Portugal, while also making 43 appearances where he delivered five assists.
The holding midfielder is said to be happy in Spain despite his side missing out on European football.
Manuel Pellegrini has held an interest in William Carvalho before so it comes as no surprise that West Ham have been linked with a move for the midfielder. The Spanish publication claim that a move for the Portuguese international all depends on whether or not Declan Rice is at the club next season. At this current moment in time, it looks more than likely that Rice, 20, will remain at the London Stadium. After impressing for England against Holland, other clubs are certain to be interested in the young midfielder. At 27-years-old Carvalho offers great experience in the middle of the park and was integral in a Betis side that progressed to the knockout stages of the Europa League. It would all depend on the price of Carvalho whether or not this deal could happen, with reports suggesting that Pellegrini will need to sell fringe players to fund extra moves in the window. With the Hammers reportedly on the verge of a £40million move for Pablo Fornals, a move for Carvalho looks like being just a rumour for now.