The former Bolton and Blackburn manager arrived in east London in the off-season of 2011 and has since taken them from the Championship back up into the English Premier League, where they sit in 12th.
Despite that success, the West Ham board have been reluctant to extend Allardyce's contract, which expires at the end of season, instead preferring to wait until the end of the campaign to discuss terms.
Speaking after West Ham's 1-0 win at Stoke, the 58-year-old said he would remain at Upton Park provided West Ham avoid the drop.
"Staying in the Premier League is everything about my future," Allardyce told reporters. "That is all I have had to say over the last few weeks.
"It is where I want to be and where I want to apply my skills because I like the euphoria, excitement and pressure that it brings.
"It is the best league in the world and the most entertaining, so plying your trade in it is what you want to do."