However, City boss Steve Bruce rejected the idea of a player exchange as he hopes to sign Arsenal central-defender Matthew Upson.
Venables has since told Bruce he is interested in a deal involving only Lazaridis - who played under the Leeds boss during his time in charge of the Australian international squad.
Lazaridis' contract at St. Andrew's runs out in the summer so Birmingham could be set to cash-in on a fee for his signature now.