However, the ageing midfielder looks set to move to Fratton Park to join Harry Redknapp's Pompey revolution as the former West Ham boss attempts to steer the south-coast club into the Premiership.
Sherwood's snub would be the latest in a long line for the West Brom chief having already failed in bids to sign Tony Sanneh, Roberto Rios and Salva Ballesta, although he is still hopeful of completing the capture of Macedonian Artim Sakiri.