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.
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."
While Allardyce expects to stay, the future of his players is not so certain. High-profile Liverpool loanee Carroll has admitted he is unsure as to where he will be next season, while a number of other West Ham players' deals soon come to an end.
"We have Andy and the other loan players - Marouane Chamakh, Emmanuel Pogatetz," Allardyce said. "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."
Jussi Jaaskelainen is another whose deal runs out this summer, although an option of a further year with the Hammers is set to be activated.
"When I first came here I signed a contract that if we stay up I would stay on so there's nothing to sign," the former Bolton goalkeeper said. "I'm happy but we're obviously not over there yet - staying up. So I don't really have to do anything about it apart form make sure we stay up.
"It was always going to be difficult when you've had 14-and-a-half years at one football club and you're wondering what's going to happen but I've really enjoyed it. Big Sam was the reason why I wanted to come here. When he gave me the phone call straight away I thought it would be fantastic to play with him again because I know what kind of stuff he does with his players."
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