Blues boss Alex McLeish has made it clear signing a quality forward is his number one priority during the current transfer window.
Keane has slipped down the pecking order at White Hart Lane and is desperate to play regular first-team football. He has also recently been linked with a move to relegation-threatened West Ham although no concrete movements have been forthcoming.
Blues' lack of goal power has been the main reason why they have been locked in a survival battle during the first half of the season.
Midfielder Craig Gardner is the top scorer with just five goals and McLeish has become frustrated at his side's inability to convert their chances.