The club released a statement on their official website claiming that under new regulations, they will be punished if they go over wage allowance, which Sullivan admits the club are edging closer to.
"Sam [Allardyce] and I are working tirelessly on identifying new targets to add to what has been a very good window for West Ham United thus far," said Sullivan. "However, the new rules state that if a team exceeds the new wage limit they could be hit with a points deduction.
"As we are now close to that limit, players can only be brought in if there is money left in the wage budget, meaning any new signings at West Ham are dependent on other players leaving the club.
"I have seen the suggestion that we should just give away or sell a few fringe players to free up the wages but I must stress this is easier said than done and despite our hard work over the summer, it just hasn't been possible yet."
The Hammers have acquired the signatures of five new players this summer.