Allardyce is keen to find attacking signings next month.
He told whufc.com: "I've said before it's not an easy task to bring players in at this time of the season. We're looking at loan players rather than a permanent and I think it makes it that little bit more difficult. Who knows if someone turns up and wants to talk then it can happen very swiftly.
"When David Sullivan and David Gold make a decision, the reaction to the decision is almost immediate and they try and get the deal done, we don't dither. If we can't, we say 'thank you very much' and get on with it."