West Ham have been linked with a move for forward reinforcements due to Andy Carroll’s heel injury, which has kept the England man out of action so far this season.
Ricardo Vaz Te looks set to depart Upton park, with Modibo Maiga so far struggling in attack so far.
With Carroll ruled out, Maiga started in attack against Stoke on Saturday, but the former Sochaux man struggled as the hosts created very few clear-cut chances in the 1-0 defeat and Allardyce lamented the difficulty of signing new players so late in the transfer window.
He said: "When you’ve got to overlap one with another coming in to create the finances for the one coming in then they almost have to sign at the same time.
"I can’t let that player sign for an opposition side until I know definitely that the player I’m bringing is going to sign for us.
"Until he has put his signature on the paper he hasn’t signed for us even if he is in the building. It makes life extremely difficult for us, but it is also difficult to find players of the quality to play at this level.
"A player we bring in we might need or want to play in the first game at Southampton and if we’re going to get anyone they’ll be from outside of this league."
