Cole is currently available as a free agent after reaching the end of a previous deal at West Ham United.
Various clubs were linked with an approach over the summer, but the England international is still without a club.
He has returned to training with West Ham as a result, in an effort to earn fresh terms, and Sam Allardyce has admitted to being keen on getting the powerful frontman back on board.
With it expected that he will re-sign for the Hammers, Redknapp concedes that he will have to look elsewhere for support to Charlie Austin - his only fit forward.
He said after a 1-0 victory over Yeovil Town on Saturday: "We want a striker, but clubs won't let them out on loan.
"We need help up front, that's for sure.
"Charlie's doing a good job but he needs some help. He can't keep doing it in every game, we need to take the pressure off him.
"Carlton's a great player, but I think he's going to sign for West Ham."