The Hammers have been busy bringing in new faces this summer, with Mauro Zarate, Cheikhou Kouyate and Aaron Cresswell all agreeing moves to Upton Park in recent weeks, but Allardyce believes that there is still more work to be done.
"I think there are three or four positions - it depends on the budget," the boss told West Ham TV. "You would say there is still room for a young central defender, particularly a left-footed one because we do run with three and not four. Ideally, you would have four.
"You would also say we need another left-back to go along with Aaron and I think a front-line player and the possibility of a midfield player as well."