Allardyce has also ruled out sending Yannick Bolasie on loan to build up his match fitness, having missed more than a year through injury, but says that Kevin Mirallas may be granted permission to leave Goodison Park.
"One at a time will be the order of the day," he told reporters when asked about any further incoming activity. "Hopefully by the end of January we will have got some business done and be a stronger squad for it. We need some pace in the side so we are trying.
"Yannick is way ahead of where he should be. [But] he shouldn't be starting yet. It's ludicrous to think we're going to let him go on loan. That's what we have to deal with. That speculation creates massive problems for all managers. It's very disconcerting, particularly for a player if he hears that message."
On the uncertain future of Mirallas, Allardyce added: "It depends on many factors. It depends on whether Kevin wants to go or does he fancy the club that comes in for him and do we agree with the fee that is being offered.
"That transfer may well occur, as with many players in January. You never say never to what goes on in the January window."