West Ham boss Big Sam wants another midfielder on board after Gary O’Neil’s failure to agree a new deal.
Baggies chief Steve Clarke told Dorrans in January he could find a new club after losing his first-team place.
The Scotland international stayed and ended the season with 20 Premier League appearances but now looks set to go if a decent offer comes in.
The Hammers face competition with Norwich and newly-promoted Cardiff also keen on the 26-year-old.