The former Tottenham boss says he admires the 30-year-old's talents but admits the Hammers' injury problems make any potential January move difficult
Cole, 30, was released by West Ham at the end of last season, but rejoined the London club in October on a short-term deal.
The former Chelsea man's contract expires this month and Redknapp is hoping to lure him to Loftus Road.
Redknapp told BBC London: "It's difficult as he belongs to West Ham still. 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."
Cole has scored three goals in 10 appearances for West Ham since returning to the club.
Rangers ended a run of three games without scoring as they came from behind to beat Doncaster Rovers 2-1 in the Championship on New Year's Day.