Although Allardyce met his first target of getting the club promoted to the Premier League last season, it is believed that co-owners David Gold and David Sullivan are waiting to see whether he can keep West Ham in the top flight of English football before offering him a new contract.
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Allardyce told reporters: “This is a both-party agreement and both parties will sort it out privately and confidentially when the time is right.”
The former Bolton manager is currently in the second year of his contract at the Boleyn Ground, and despite co-chairman David Gold revealing on Twitter that he backs Allardyce, former Hammers star Paolo Di Canio has been linked with the club after resigning from his post as Swindon manager.
West Ham host Tottenham on Monday evening as Allardyce aims to bolster their chances of Premier League survival.