The Hammers are sixth in the league table at the moment with 59 points from 35 matches.
The London outfit are five points behind Manchester City, who are currently fourth in the standings and occupy the final Champions League spot, but they have a game in hand.
West Ham maintained their chances of finishing in the top four with a 3-0 victory over West Bromwich Albion away from home at The Hawthorns on Saturday afternoon.
Manchester United drew 1-1 with Leicester City at Old Trafford on Sunday, while Manchester City went down 4-2 to Southampton away from home at St. Mary’s Stadium.
Also on Sunday, Liverpool suffered a 3-1 defeat to Swansea City away from home at the Liberty Stadium.
With results at the weekend going their way, West Ham co-chairman Gold has suggested on Twitter that Slaven Bilic’s side's dream of finishing in the top four is still alive.
Liverpool lost Man City lost Man United drew West Ham won. The dream is still alive. dg— David Gold (@davidgold) May 2, 2016