McLeish has revealed how close he went to landing the Belgian.
"I spoke to Dick Advocaat about him. Dick was his coach for Belgium and had seen a lot of him when he played in Holland," he told the Scottish Sun.
"His exact words to me were 'Alex, if you can get him for between £3m and £5m, I'd take him blind'.
"I drove Dembele's agent, a guy called Rodger Linse, to the station. We had a long discussion about how a move to a club like Birmingham would be perfect for him because it would give him a platform, with the possibility of moving on in the future.
"Everything seemed set and I thought we had Dembele, but we were gazumped by Fulham and he went there."