Allardyce has guided the club back to the Barclays Premier League and West Ham now sit eighth in the table after last weekend's 3-1 win over European champions Chelsea.
But the 58-year-old knows he must continue to succeed and appease the club's supporters if he is to lead the move across east London from Upton Park to the Olympic Stadium.
They host Liverpool on Sunday and Allardyce said: "The only way I can continue to be the long-term future of West Ham United is to win football matches," he said.
"Around the corner you are always aware of how this game might change.
"You never know what is around the corner. It happened to me at Newcastle, it has happened to me at Blackburn, so you never ever know.
"For me it is about winning football matches and the future will be rosy for me and the football club if we continue to win.
"I'll be here a long time if we continue to win, if we don't then my job will come under scrutiny like everyone else."
West Ham last week