Redknapp failed in a bid to take the 25-year-old Bolton Wanderers defender to White Hart Lane in August.
However, the boss has revealed that he has not given up his pursuit on Cahill, whose contract at the Reebok Stadium expires next summer.
"We were able to negotiate a deal with West Ham for [Scott] Parker, but we couldn't get a deal done for Cahill," the Daily Mirror quotes Redknapp as saying.
"That's not to say we won't try again in January. If the chairman can reach an agreement with Bolton I'd love to bring him here."
Cahill started alongside John Terry during England's 2-2 draw with Montenegro.