Despite pledging his future to the club in the immediate aftermath of their relegation, Foster is thought to have had a change of heart since and last week refused to travel to Portugal for a pre-season training camp along with team-mate Craig Dawson.
Watford have already seen one bid for the former Manchester United man, thought to be worth around £1m, turned down as the 'Baggies' hold out for closer to £3m for one of their best players.
Now 35, Foster has just one year remaining on his contract at the Hawthorns, with Darren Moore reportedly chasing Manchester United's Sam Johnstone, who they tried to sign last summer, as a replacement.
Johnstone impressed in the second tier on loan at Aston Villa last term, but is surplus to requirements as Old Trafford, with Stoke's Lee Grant expected to join the club in the near future as back-up for Sergio Romero and David De Gea.