Norgaard missed the Bees' 3-1 defeat at Tottenham Hotspur last weekend with "a minor injury", but Frank revealed after the match that he is "very confident" that the Dane will be fit to return against the Hammers.
However, Brentford are still having to cope without Yoane Wissa (ankle), Josh Dasilva, Igor Thiago (both knee), Mathias Jensen (calf), Aaron Hickey (thigh) and Gustavo Nunes (back) due to injury, while Rico Henry (knee) remains doubtful.
After using a three-at-the-back system in the last two league matches, Frank may consider reverting to a four-man defence this weekend, with could see either Kristoffer Ajer or Vitaly Janelt tasked with operating a left-back and Mads Roerslev recalled on the right. Sepp van den Berg could be sacrificed, though, with Ethan Pinnock and Nathan Collins the most likely duo to start at centre-back.
Should Norgaard be deemed fit to feature, he could slot straight back into a three-man midfield, with Janelt, Mikkel Damsgaard and Yegor Yarmolyuk all set to battle for the remaining two starting spots.
Keane Lewis-Potter could be handed a start in the front three after playing at left wing-back in the previous two games, while Fabio Carvalho will hope to fend off competition from Kevin Schade once again to link up with star forward Bryan Mbeumo, who is tied with ex-teammate Ivan Toney as the club's most productive player in the Premier League with 47 goal involvements (21 goals, 26 assists).
Brentford possible starting lineup: Flekken; Roerslev, Collins, Pinnock, Ajer; Damsgaard, Norgaard, Janelt; Mbuemo, Schade, Lewis-Potter