The Old Trafford outfit moved up to third in the table last Saturday courtesy of a 3-1 win over struggling Leicester City, with fourth-placed Southampton losing at home to Swansea City the following day.
Van Gaal's men followed that up by coasting to a 3-0 FA Cup fourth round replay win over League Two outfit Cambridge United on Tuesday to set up a clash at Preston North End.
Former Netherlands coach Van Gaal on Friday vowed to contest a Football Association charge for comments made about referee Chris Foy after the FA Cup draw with Cambridge at the Abbey Stadium.
The Manchester United manager's immediate attention, though, is on securing three points at Upton Park against a West Ham side that suffered a 2-1 defeat in September's reverse fixture despite Wayne Rooney's red card.
Van Gaal said: "After we beat Leicester, we were third in the league, and after that we beat Cambridge and are in the next round.
"Now we have to continue and all players know this is true.
"It is not so easy because we have to play away in London against West ham and it was a tough game in Manchester.
"It shall not be easy but we want to continue and we have to win in London.
"I am only satisfied at the end of the season because now to be third and in next round doesn't count.
"We have to play a lot matches and also Spurs and Arsenal are in our back, one point or two behind. A lot of matches to go and still three to go to the [FA Cup] final. That is our goal."
Sam Allardyce bemoaned West Ham's injury problems ahead of the clash in the capital, but urged his side to frustrate United.
"Man United have had some very good results recently and the beauty of them is the goalscoring ability in their squad," the West Ham manager said.
"Our aim is to limit that as much as possible. We need to be tactically astute and try to cause them a few problems."
Allardyce has injury concerns over James Collins, Winston Reid, Guy Demel, Diego Poyet, Doneil Henry and Andy Carroll.
Diafra Sakho will be available for selection following a week in which West Ham were fined fined £71,000 and reprimanded by FIFA for playing the Senegal striker during the Africa Cup of Nations after he had pulled out of the tournament due to a back injury.
Van Gaal will again be unable to call upon Michael Carrick, who will miss the encounter against his former club due to a calf problem.
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