The Hammers are claimed to be considering a bid but will face competition from Wolves, Napoli and Paris Saint-Germain to sign the Portugal international.
Sporting do not want to sell the 30-year-old, who still has over four years remaining on his contract, but any interested clubs can open negotiations if they meet the player’s release clause of £30.66m.
The Hammers are in the market for a new goalkeeper with the loan deal of Joe Hart coming to an end and the possibility of Adrian returning to Spain but no decisions would be made until the manager decision is resolved and a new head of recruitment is appointed.