Cole's contract at Upton Park expires later this month and as yet there has been no news on whether the deal will be extended or not.
West Ham must now make a decision on Cole's future or risk losing the player for nothing when his deal expires after the clash with Newcastle on January 18th.
Redknapp is keen to bolster his attacking options in January and he is an admirer of former Chelsea man Cole.
"It's difficult as he belongs to West Ham still," said Redknapp.
"Sam Allardyce has his own problems with injuries and everything there.
"Carlton is a good player and I like him. He is one of many players we are looking at but if West Ham decide to keep him it can't happen."