The Republic of Ireland captain has not featured much for Spurs this term, having slipped behind Peter Crouch, Roman Pavlyuchenko and Jermain Defoe in the pecking order.
Redknapp confirmed that Birmingham made a £7 million offer at the beginning of the month, but no agreement had been reached.
Although Keane joined Celtic on loan last year Redknapp stressed that he had no intension of letting Keane go out on loan again this year. He told Sky Sports News: “I think West Ham wanted to loan Robbie but he’s not for loan, it wouldn’t be a loan anywhere. We couldn’t loan him out again, he went out on loan last year, so if somebody wants him, they’re going to have to buy him now.”