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."
It has been reported: ¿The west London side's promotion push has been based on their mean defence, which has been breached only 14 times, and Redknapp is adamant they will bring in another striker. "I'm looking for a proven goalscorer and someone who can come in and do the job," he said. A quick look at the stats for Carlton Cole : Starts for West Ham in past 5 seasons ¿ 128. Appearances as sub ¿ 49. Total goals scored for West Ham in past 5 seasons ¿ 50. I know Harry has difficulty with reading, writing and arithmetic. He said so under oath. But surely someone can tell him that if Carlton Cole has scored only 50 goals in 5 seasons, he is not likely to get many more than 5 in all competitions, in the half a season that is left. Proven goalscorer, indeed! Eddie Murray- denser