West Ham United are attempting to sign a striker this summer.
The Hammers have been looking for a forward ever since last term finished, and they have lodged a wide range of offers.
West Ham have made bids for the likes of Alexandre Lacazette, Callum Wilson and Carlos Bacca.
However, none of their attempts have proven to be successful - and Sullivan admits that it may be a case that West Ham are not able to sign a striker the summer now.
”I would say to people if we don’t bring anyone in it is not the end of the world as we were the fourth highest scorers in the Premier League last season – and we haven’t lost a striker,” Sullivan said.
“In a perfect world I would like to think we will bring in a top class striker but we’ve all got limits on what we can pay.
“I am a little concerned because I’d like to have signed one by now. But it is what it is.”
West Ham made signing a striker their top priority this summer, but they have struggled to get deals over the line.
The Hammers have strengthened other areas of their squad, though, with the additions of Sofiane Feghouli and Gokhan Tore catching the eye.
West Ham finished in seventh place last season, and they are looking to push on even further in the coming campaign.
Bilic’s side are expected to invest a large amount of funds before the end of the transfer window, with more players set to arrive at the Olympic Stadium soon.