The duo have signed for the club in the last few days, with Kongolo making his debut in the FA Cup win over Bolton last weekend.
Pritchard signed from Norwich for £11million and Wagner may use him off the bench at the John Smith's Stadium.
Both Michael Hefele and Phillip Billing are back in training and ready to push for first-team action, but Chris Lowe, Martin Cranie and Collin Quaner will all miss out.
The Terriers have not won at home in the Premier League since December 9 but West Ham have only recorded one away win in the league this season.
Hammers coach David Moyes looks set to recall Marko Arnautovic after he recovered from a hamstring strain. Defender James Collins is also back in training but Winston Reid is a doubt with a groin issue and Aaron Cresswell misses out due to a back complaint.
West Ham are looking to do the double over the Terriers this year after they recorded a 2-0 win in September at the London Stadium.