The sixth-placed Hammers go into the game at the Britannia knowing a win would secure European football at the Olympic Stadium next season.
Bilic's high-flying side have enjoyed their best ever Premier League season in terms of points return and goal difference.
And they go into the match with Mark Hughes' side off the back of a thrilling 3-2 win over Manchester United in the last ever game at their beloved Boleyn Ground home of 112 years on Tuesday night.
Stoke have had extra rest and West Ham spent a lot of energy in what was an emotional night in East London last time out.
'They want to go the extra mile'
But co-owner Gold has told the club's official website his side can finish the season in style.
"You can see the energy and determination from our players and I go up to Stoke in our final game on Sunday believing we can come away with three points," Gold told whufc.com.
"Even though Stoke have been on a tough run, they will want to end the season on a high note, but I think we are a good side and we have players who want to win.
"They want to go the extra mile. We saw that against Manchester United and the players gave everything."
Hammers the form side
So Gold doesn't feel the tremendous effort and emotion that went into their historic win over the Red Devils will have any impact on the side's performance levels against a Stoke team with little but pride to play for.
The Potters have enjoyed a good season but haven't won for seven games since a 2-1 victory at Watford back in March.
The Hammers meanwhile were unexpectedly thrashed 4-1 by Swansea in the penultimate game at Upton Park which ended their Champions League hopes, although it was their only defeat in the last 12 Premier League games.
The sides could not be separated when they met at Upton Park earlier in the season playing out a 0-0 draw.