The Hammers boss has revealed the club's intentions of keeping hold of the 24-year-old, who moved to Upton Park on a season-long loan deal from Liverpool in the summer.
While the Premier League outfit want to finalise a transfer at the end of the season, Allardyce has claimed that financial fair play rules would wipe out their chances of signing the frontman.
"I think the hardest thing is the overall negotiation that needs to go on so that it can be sustainable," Allardyce told Sky Sports News. "I'll still point to financial restrictions being implemented next season, which could blow the whole deal in one go.
"In one fail swoop the new financial restrictions mean that Andy Carroll can't sign for us from Liverpool because it's too expensive. I might not be able to afford Andy Carroll full stop, even if I wanted him, even if the chairmen wanted him, which we do."
Carroll recently admitted that he is open to staying with the Hammers.