A left-back had previously been targeted by Allardyce but, with less than a fortnight to go before the January 31 deadline, the former England boss is now more concerned about moving fringe players out of Goodison Park.
Asked at his weekly press conference if fans can expect another arrival, he said: "No, I don't think so. We would be more in the terms of where we are at the moment [and looking at] moving players on.
"The squad is too big. There are 33 players here at the moment and from my point of view reducing those squads numbers is important for me. We don't know who those players are because you are waiting for other clubs to show an interest. But moving a few players on is the order for us."