When it came down to the nitty gritty ahead of the transfer deadline day, the Belgium international threw his lot in with Fulham.
Blues had also agreed a £5 million fee with the Dutch club.
McLeish told the Birmingham Mail: "Dembele was one that we worked on for a long time. We tracked him for over a year. Dick Advocaat was his manager at both the Belgium national team and AZ Alkmaar, I spoke to Dick about him a year ago.
"If it was up to me, if I was doing the negotiations, he would have been signed. Done.
"But there are other circumstances, factors, which make it difficult. We believe the agent had told his father and Dembele that we offered less than we actually did offer. That was why Dembele talked to Fulham. So we don't know, maybe the agent on the other side of things was getting more money in the other deal.
"It's little things like that - but I can't say for sure. It's a change from my day. I used to go in and negotiate with guys like Sir Alex Ferguson and the chairman myself. There were no agents involved."