Brentford failed with a bid for the 20-year-old - who is out of contract in 2023 - during the January transfer window.
The Bees are still considered favourites to sign Johnson, who will not sign a contract extension with Forest if they fail to win promotion to the Premier League.
But Leeds will move strongly for the Wales international should they stave off relegation, per the Daily Mail.
Johnson has notched 15 goals and nine assists in the second tier this term.
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