West Ham boss David Moyes wants to add more firepower to his squad to keep a top four push on track and the Hammers have been linked with a host of strikers.
It has been suggested that they want Nunez, with talk of a fee even being agreed to bring him to the London Stadium.
However, according to Portuguese journalist Pedro Sepulveda, Nunez will not be leaving Benfica before the transfer window slams shut.
It is claimed that the Uruguay international will remain at the Estadio da Luz.
Newcastle have also been linked with Nunez and it is suggested that they are the only club to show substantial interest in landing the striker.
The 22-year-old is a key man at Benfica and has been on fire in the Portuguese league this season, scoring 15 goals in just 16 games.
Nunez has scored two hat-tricks in the league this season, along with registering two braces.
Benfica have him on a contract until 2025.
