Keane joined Liverpool from Spurs for £20million in the summer, but it is not expected that Redknapp will bid anywhere near that.
Keane has failed to make an impact at Anfield and Liverpool boss Rafael Benitez has lost his patience with the striker, according to News of the World.
Benitez will also be looking to offload Italian defender Andre Dossena and Phillip Degen in the January transfer window.
