The Hammers have been strongly linked with Andy Carroll since the end of last season, but Allardyce is still unsure if they will be able to capture the target man before the window shuts.
"Our problem is I have since moved on financially. When I first went for Andy Carroll I could afford him, whether I could now is a different matter," he told reporters.
Allardyce went on to confirm that he is looking for one more player in to add to his squad to go with newly signed Matt Jarvis who joined from Wolves last week, he said
"At the very best I think one player will be joining us before the deadline tomorrow.
"Hopefully we can achieve that and get a quality player who could add to the team and the squad and make an impact almost immediately."
Both Mark Noble and Carlton Cole have been linked with moves away from Upton Park but Allardyce said there have been no bids and they wouldn't be entertaining any.
He added: "We've had no bids. Would we welcome any bids? No."
Another player reported to be leaving the Premier League new boys is Nicky Maynard who scored for the club in the Capital One Cup on Tuesday. Maynard only signed for The Hammers in January but the manager remained coy on the transfer.
He continued: "There's been some interest in Nicky but there has been nobody that has encouraged us to try to sell, that goes for all the players."