The Baggies are on the verge of finalising a deal to sign Foster on loan initially, with a view to a permanent transfer next summer.
The news comes on the same day as Birmingham acting chairman Peter Pannu's warning to fans to expect several high-profile exits with the club's finances under threat following owner Carson Yeung's arrest on money-laundering charges.
Ben there, done that: Ben Foster is set for a switch to West Brom
Removing Foster from the wage bill is on the agenda with West Brom boss Roy Hodgson looking to capitalise after selling Scott Carson to Turkish side Bursaspor last month.
Hodgson has been linked with West Ham's Robert Green but Foster was always among his leading targets.
The former Manchester United player had an outstanding first campaign at St. Andrew's after a ?6-million move.
Arrested: Owner Carson Yeung's troubles are affecting Birmingham
He helped the Blues to win the Carling Cup - their first trophy for nearly 50 years - but was powerless to stop them from being relegated from the Barclays Premier League.
Foster, 28, has made it clear he would prefer to remain in the Midlands and a switch to Albion would fit the bill.
Prepare for the worst! Yeung troubles will force Birmingham to sell stars, warns PannuBirmingham space to let, central location: City unable to find shirt sponsor following relegationScotland star McFadden attracting interest as Blackburn and Everton plot movesWe need a shake up! Pulis targets glut of new signings to revitalise Stoke