Redknapp admitted QPR chairman Tony Fernandes is already in talks to sign former Chelsea striker Nicolas Anelka, who is hoping to return to Europe after terminating his contract with Chinese side Shanghai Shenhua.
Redknapp said: "We can't wait. The chairman is going to have to bite the bullet a bit and get on with what we have got to do.
"We really need to be doing our business right at the start of January. It is no good a club trying to ring up to do business on the last day of January - it's too late. We are going to be finished by then."