The Hammers have had one bid rejected for the 25-year-old, but manager Slaven Bilic is hopeful of concluding a transfer.
Carvalho was part of Portugal's triumphant Euro 2016 squad and also featured in their third-place finish at the Confederations Cup this summer.
He has scored one goal in 37 international appearances.
Bilic signed forwards Marko Arnautovic and Javier Hernandez, for £20m and £16m respectively, and goalkeeper Joe Hart on loan this summer.
However, a side containing Hart and Hernandez lost 4-0 at Manchester United in their Premier League opener on Sunday.
Sofiane Feghouli has joined Galatasaray for a reported £4m, after a season at the Hammers.
The Algerian winger scored four goals in 27 appearances, after joining from Valencia in June 2016.
West Ham are closing in on the signing of Sporting Lisbon midfielder William Carvalho for an expected £30m.