The Bees had allegedly agreed a club-record deal to sign the 18-year-old Norway international for around £31.5m, including add-ons, earlier this week.
However, Nusa's medical is said to have identified knee and back issues which have raised concerns among Brentford chiefs, and the teenager has since returned to Belgium.
According to the Evening Standard, Brentford are requesting for further medical information about Nusa from both Club Brugge and the Norwegian Football Federation.
Although Nusa is widely regarded as one of the brightest prospects in Europe, the Bees are said to be cautious of parting with such a significant amount of money on a youngster who has no Premier League knowledge and minimal experience of playing at the highest level.
Nusa had been attracted by the prospect of gaining regular first-team football with Brentford in the Premier League and making further developments with an established English club in the infant stages of his career.
However, Brentford's decision to put their move for Nusa on hold could open the door for the likes of Chelsea, Tottenham Hotspur and Newcastle United to reignite their interest in the summer.
Nusa joined Brugge from Norwegian side Stabaek in 2021 and was primarily used an impact substitute last season under former boss Scott Parker, but since the arrival of current manager Ronny Deila, the forward has been given more first-team opportunities.
Indeed, Nusa has started 11 of his 28 appearances for Brugge in all competitions this season, scoring four goals and providing three assists.
Brugge's No.32 received his first senior international call-up for Norway in September last year and he recorded a goal and an assist on his debut in a 6-0 friendly win over Jordan, before registering three assists across two Euro 2024 qualifiers against Georgia and Cyprus.
Brentford's interest in Nusa comes at a time when star striker Ivan Toney faces an uncertain future at the club, although a potential big-money transfer is seemingly more likley to take place in the summer.
Thoams Frank's side have made three signings so far in the winter window, with left-back Sergio Reguilon arriving on loan from Spurs, teenage midfielder Yunus Emre Konak joining on a permanent deal from Sivasspor, and goalkeeper Hakon Valdimarsson signing from Elfsborg for around £2.5m.