The Hammers have already had one bid for the midfield powerhouse rejected, but Slaven Bilic's side are now close to finalising a deal worth an initial £30m.
Portuguese media claim Carvalho is keen on a move to the Premier League and will travel to London on Monday.
The 25-year-old was a key figure in Portugal's success in the European Championships in France last summer and now looks set to become West Ham's sixth new arrival of the current transfer window.