The Denmark international was forced off with a foot problem in an FA Cup clash with Wolverhampton Wanderers on January 5 following a challenge by Joao Gomes.
As a result of the injury issue, Norgaard was forced to miss the replay with Wolves and the Premier League win over Nottingham Forest.
Having been without their captain for the last two matches, Brentford have received a boost ahead of Wednesday's meeting with Spurs.
Speaking to reporters at his pre-match press conference, Frank said: "Norgaard is involved in the squad tomorrow and that's very positive."
"It's been a short turnaround after the injury he got against Wolves in the first leg of the FA Cup game."
While the midfielder may be available for the midweek contest, Brentford are still having to cope with a number of absentees.
Aaron Hickey, Rico Henry, Bryan Mbeumo and Kevin Schade remain sidelined through injury, while Sergio Reguilon is ineligible to face his parent club after arriving on loan from Tottenham earlier this month.
Saman Ghoddos is at the Asian Cup with Iran, while Frank Onyeka and Yoane Wissa are at the Africa Cup of Nations representing Nigeria and DR Congo respectively.
Away from Wednesday's fixture, Frank hopes Brentford can strengthen their squad before Thursday's deadline, have already recruited Yunus Emre Konak, Hakon Valdimarsson and Reguilon.
Frank added: "It could be difficult, but we have been working on players who could also be possible in the summer, sometimes we don't get them the first time, we get them the second time."
Brentford were reportedly on the verge of signing Antonio Nusa from Club Brugge, but the move is now in doubt due to issues surrounding the player's medical.
The Bees are also believed to be scouting Plymouth Argyle winger Morgan Whittaker, who is attracting interest from Fulham and Lazio.