The Mirror says Redknapp is aware Gallasâ€™s future at the Emirates remains in doubt.
Manager Arsene Wenger has stripped Gallas of the captaincy and is reviewing the playerâ€™s future after he publicly accused team-mates of in-fighting, insulting behaviour and lacking bravery.
While publicly peace has broken out, Gallas still appears to be heading towards the Arsenal exit.
Spursâ€™ move for Gallas revives memories of Sol Campbellâ€™s switch from White Hart Lane to join the Gunners in 2001. But signing an Arsenal player will not trouble Redknapp.