The Hammers have been linked with a sensational swoop for former striker Demba Ba after the Senegal international struggled to make an impact at Chelsea following his January move.
Carroll is already a fitness concern for the imminent Premier League campaign as the England international continues to recover from a heel injury which he suffered on the final day of last season.
But Allardyce insists he has spent his transfer budget, and as a result, the Hammers boss won’t be bolstering his attacking options.
“No, my budget is finished now,” Allardyce told a news conference on Thursday.
West Ham striker Modibo Maïga has been linked with a return to Ligue 1 in recent days as Saint-Etienne reportedly weigh up a bid for the Mali international.
But Allardyce is adamant he won’t be selling the 25-year-old forward, who moved to Upton Park in 2012, unless the east London side receive an offer too good to refuse.
“He can’t move away because Modibo and Andy Carroll are our two front-liners here,” added Allardyce.
“Unless, the chairman says we’ve got the sort of bid that we can’t really be turning down, then he won’t be going anywhere.
He continued: “Any move depends on how much someone is offering in the first place and whether we’ve got an immediate replacement lined up.”
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