Thomas Frank has lengthy been an admirer of the 22-year-old however has failed in a primary strategy that falls wanting the Midlands membership's valuation.
Forest see Johnson as pivotal to their goals for the approaching season, having narrowly averted relegation this time period.
The membership retaining their Premier League standing has made them ready to withstand approaches from Brentford. It stays to be seen if the Bees will return with an improved provide.
Brentford are searching for attacking reinforcements after Ivan Toney was handed an eight-month ban from enjoying soccer.
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Toney, 27, was final month charged with breaching the Football Association's betting guidelines. He is unable to play once more till January 2024 and is subsequent allowed to coach together with his team-mates on September 17 this 12 months.
The Bees have a number of attacking choices, together with Kevin Schade, purchased for a club-record payment of £20million earlier this week, their earlier club-record signing Keane Lewis-Potter, plus Bryan Mbeumo and Yoane Wissa.
Brentford have additionally signed goalkeeper Mark Flekken from Freiburg as David Raya edges nearer to becoming a member of Tottenham.
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