Slaven Bilic insists West Ham have yet to secure their Premier League status and is keen to reach the "magic number of 40 points".
With four games remaining, the Hammers are 14th in the table and currently have 38 points - seven more than Swansea in 18th.
Speaking ahead of this weekend's trip to Stoke, Bilic told Thursday's press conference: "People are talking about speculation that 38 points will be enough.
"But in the history of the Premier League, it's always that magic number of 40. We have four games to play and still 12 points to play for and we want to finish high.
"It's a very demanding league, every game is very difficult but we've shown when we are good that we have a chance in every game.
"People are talking about who is safe but it is irrelevant. We have four games left, a big game on Saturday and we are looking for points.
"There is a gap between us and mid-table, it is a small gap but with four games to go we are talking about 12 points and we have to concentrate on our next game.
"We are approaching them as four cup finals."
Bilic also spoke about Romelu Lukaku, with West Ham one of many clubs linked with the Everton striker.
He added: "He's one of the best strikers, not only in the Premier League but in Europe. People forget how young he is because he has been on the radar for a while.
"He's been scoring goals since West Brom, when he went on loan from Chelsea and then in every season for Everton he's been scoring goals but he's been getting better and better.
"That's why he's been linked with a lot of big clubs. Everton have done a great job to keep him. It shows how good and how ambitious they are."