Brunt picked up a knee injury in training on Monday after featuring as a late substitute in the previous day's 1-0 victory over Norwich City.
The Northern Ireland international is rated 50/50 to make the trip to the Liberty Stadium at the weekend and first-team coach Michael Appleton does not expect the injury to prove to be serious.
"Apart from a few bumps and bruises that most people got on Sunday I think the only one that is 50/50 is Chris Brunt," Appleton told the club's official website on Wednesday.
"He picked up a knock on his knee in training on Monday. It is nothing serious, it is more precautionary.
"He seemed to be in a reasonable frame of mind yesterday (Tuesday) morning so I don't think it is too serious."
Meanwhile, Zoltan Gera continues to make progress from a summer ankle operation as the Hungarian midfielder waits to make his second debut for West Brom.
Appleton added: "Zoltan is not doing too bad at all. He's trained for eight or nine days with the players.
"Touch wood, we're getting into a situation where he may be able to have a little bit of football, whether that be with the reserves or whether or not the Carling Cup is a bit too soon, we'll see. He seems to be coming on okay."