The Mirror says Hammers boss Sam Allardyce spotted the highly-rated 26-year-old who will sign for three seasons if he passes a 'test'.
Allardyce wants competition for veteran Jussi Jaaskelainen and San Miguel fits the bill perfectly as his contract is up.
San Miguel will not be coming to settle for life in the reserves. He played 32 times for the Seville-based outfit.
His arrival puts Jaaskelainen under pressure, but the Finn will fight to keep his place - although the younger keeper looks set to eventually be number one.