The Baggies are understood to have joined Blues in holding talks with the 23-year-old, who is rated in the £5million bracket.
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."
Dembele claimed on Thursday that Birmingham had provided him with his most "concrete" offer to date.
Albion are also interested in signing Aston Villa full-back Nicky Shorey, who is one of half a dozen players made available for transfer.
Shorey joined Villa from Reading two years ago but has struggled to command a regular spot and last season had a spell on loan at Nottingham Forest.