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 took 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.
Sam Allardyce: "I wouldn't be here if we weren't playing in the Premier League next season.
"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.
"We have Andy and the other loan players - Marouane Chamakh, Emmanuel Pogatetz.
"We have all the out-of-contract players like Gary O'Neil and Carlton Cole so we'll sit down as quickly as we can at the end of the season and make decisions like that."