Slaven Bilic has identified the 25-year-old as his final key addition to his side this summer.
The Hammers have been strong in their business so far, bringing in Joe Hart, Javier Hernandez, Marko Arnautovic, Pablo Zabaleta and Sead Haksabanovic.
And with money still left to spend, Carvalho has been targeted to strengthen West Ham‘s midfield.
According to The Telegraph, an offer has now been submitted for the Portugal international worth the equivalent of €30m.
Carvalho has a buy-out clause in his contract of £36.1m and Sporting are attempting to hold out for that figure.
However, it is said they are aware Carvalho is now keen on the move to the Premier League.
Arsenal have previously shown interest, but West Ham appear close to landing their man following negotiations that have been going on for over a week.
The Telegraph add Hammers representatives are currently in Lisbon attempting to seal the deal.
And West Ham are optimistic Carvalho can be signed.
Despite the east London side being unwilling to pay as much as £36.1m, talks remain positive between the two clubs.
Carvalho is apparently aware he need to move on to further his career, having been at Sporting since the start of his professional career.
The highly-rated player is represented by Pep Guardiola‘s brother, Pere, and would offer strong competition for Pedro Obiang, Cheikhou Kouyate and Mark Noble at the London Stadium.
But while the Hammers feel there is a real chance of getting Carvalho, outgoings are needed too.
Sofiane Feghouli is due to leave for Galatasaray, while Aston Villa are after Robert Snodgrass.
