Reports have suggested Allardyce is facing the sack after a difficult season, with the Hammers leaving it until the closing weeks to secure their Premier League status.
Despite criticism from a section of the fans, Allardyce was satisfied with the club's 13th place finish, but it remains to be seen if owners David Gold and David Sullivan share this view.
Allardyce took charge of the Hammers in 2011 and immediately steered them back to the top-flight, but supporters have not warmed to his playing style and jeered a home win over Hull City in March.
The 59-year-old former Bolton boss responded defiantly to questions at the weekend, pointing to his long managerial record as proof of his success.
"If you are a manager, this is the highest level in the world," he said.
"I have competed at this level for many, many years. There's only Arsene Wenger has competed at this level longer than me.
"I know how to manage in this league and I know how to turn teams into better teams than when you first take them over, so there you go."