Reports on Wednesday suggested the Hammers were leading the race to sign Juventus forward Quagliarella, who has been tipped to leave the Serie A club this transfer window.
However, while Allardyce admits he would love to strengthen his squad further he concedes the club's coffers are now empty.
The former Bolton boss has already been busy in the transfer market this summer, bringing in Andy Carroll, Stewart Downing, Razvan Rat and Adrian.
When quizzed about a potential deal for Quagliarella, he said: "Unless the chairman managed to find out how to find some more money for me without selling anyone I've got at the moment, then there are no more players coming in at this moment.
"I've got no money left, I've got the squad I have got, so that's it. If there is a new player coming in we will need to sell some players, but I don't envisage that happening, I am not looking at doing it because I am happy with the squad I have got at the moment.
"It is not frustrating for me, it is a fact of life. There is a new set of regulations that says you have a limit on your wages, which the owners have decided to put into place.
"I have hit my limit and that is it, we move on, get on with it."