Allardyce's contract ends this summer, and despite leading the Hammers to promotion last season, chairmain David Gold has said that he must wait until the end of the current campaign.
"As [fellow chairman] David Sullivan and I have always maintained, we will sit down and discuss Sam's contract situation once our Premier League status has been confirmed and not before," Gold said on the club's official website.
"This is purely because the three of us don't want anything to distract attention from our aim of finishing as high up the Premier League table as possible.
"We went into Sunday's game with Aston Villa one place off the top 10, and that is no mean feat for a newly-promoted side."
Allardyce has been in charge of West Ham since the beginning of last season.