The Spurs boss made a late bid to complete a move for the England defender on transfer deadline day in August but the deal collapsed after the two sides were unable to agree a fee.
Bolton remain keen to keep hold of one of their most prized assets but Cahill is out of contract at the Reebok Stadium next summer and the Trotters risk losing the centre back for nothing if he fails to agree a new deal.
Arsenal, Chelsea and Liverpool have also been linked with a move for the 25-year-old defender but Redknapp is hoping a deal can be resurrected to take him to White Hart Lane in the new year.
He told the Sunday Mirror: "We were able to negotiate a deal with West Ham for (Scott) Parker, but we couldn't get a deal done for Cahill.
"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."