Berbatov has less than a year to run on his contract with the Red Devils and looks surplus to requirements after falling further down the club’s striking options following Robin van Persie’s arrival.
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The 31-year-old has been strongly linked with a move to Fiorentina, that could be crucial in Manchester City's pursuit of Stevan Jovetic.
The Hammers had been linked with a move for the former Tottenham striker but Allardyce has all but given up hope of luring him to Upton Park.
Speaking to Sky Sports News, Allardyce said: "I don't think we have got the finance for Dimitar Berbatov. The financial package for the player's salary is one I think would be beyond us."
Allardyce recently confirmed the club are unlikely to sign Andy Carroll and doubts whether there will be any more arrivals before the transfer window shuts on Friday.