The 58-year-old replaced Avram Grant at the Upton Park helm following the club's relegation from the top flight in the summer of 2011.
Allardyce confounded the critics to take West Ham up at the first attempt via the play-offs and the club now look all but certain to remain in the top flight after Saturday's 1-1 draw at Southampton.
The next campaign is already coming into focus and Allardyce expects to extend his contract past the summer to remain at the Upton Park helm.
"I wouldn't be here if we weren't playing in the Premier League next season," the former Bolton, Newcastle and Blackburn boss said.
"I always said if I don't keep them up, I won't stay. We're very close to being mathematically okay.
"I think it's highly unlikely with four home games in the last six that we're not going to pick more points up.
"We are going to be safe and playing in the Barclays Premier League next season so my planning will be done as quickly as possible and we'll get on to the contract, which I'm sure I'm going to sign."