The Baggies have joined Brum in holding talks with the 23-year-old, who is rated at £5million.
City boss Alex McLeish is convinced Dembele will provide the kind of extra quality he is looking to add to his team.
He said: "Dembele is top quality but I'm advertising him to everyone else by speaking about him.
"It's difficult when someone has got options and he is a top player. The player maybe knows as well.
"Some perhaps have a little self doubt but the very top players don't have that.
"To bring in those kind of guys, to attract those kind of players to Birmingham, obviously there's a lot of money involved and, at times, big wage demands.
"But that's the ambitions I have and I would like to try and attract quality to this football team, enhance the quality factor in the team we already have."