The Blues boss revealed that Blues had enquired about the centre-back before he was targetted by Bolton Wanderers.
Davenport looked set for a move to The Reebok but the deal broke down after personal terms failed to be agreed.
Now, McLeish is unsure whether or not Blues will renew their interest in the 26-year-old former Coventry City and Tottenham defender.
"I will have to pose the question to (managing director) Karren Brady, she had been talking with West Ham United and we left our proposal with them," McLeish told the Birmingham Mail.
"Whether they now come back to us, that's a possibility."