Allardyce's newly-promoted Hammers currently sit 11th in the Premier League table, above a number of established top-flight sides including Liverpool, Aston Villa and Fulham.
Earlier in December, West Ham were confirmed as the 'preferred bidders' to take over the Olympic Stadium site in 2015 and Allardyce is eyeing the stadium move as a potential milestone in his management at the club with a view to establishing himself as "one of the longest-serving managers around".
Allardyce told the Daily Express: "For every manager, the sack is just around the corner but the Olympic Stadium is a nice light at the end of the tunnel.
"It would be a massive achievement for anyone to stay at a club that long these days. But after a number of experiences, you get confidence in your own abilities. If you don't have that, you won't survive."
In his last two jobs, at Blackburn and Newcastle, Allardyce was sacked following protests and abuse from fans, but Allardyce stated his belief that he has gradually won over any Upton Park sceptics.
He said: "Even when we've lost, the crowd have appreciated what we've tried to do. The Chelsea turnaround (in a 3-1 victory at Upton Park) was a huge booster for everybody."
Allardyce is in the final season of a two-year contract with the Hammers, although a decision on his future is thought to be unlikely to be made until West Ham's Premier League safety is secured.
West Ham currently sit eight points off the drop zone after 17 league games.
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