The Bees are on the hunt for additions in January, with a number of their players of interest to clubs.
Toumani Diagouraga has already left to join Leeds United, while James Tarkowski and Alan Judge could head out of the exit door.
However, Brentford are reportedly determined not to see their squad weakened and they feel that Paterson would be a good addition.
The 24-year-old has scored five times in 20 matches for Huddersfield since joining on loan from Forest in September.
Brentford boss Dean Smith also knows Paterson well, as the pair worked together at Walsall earlier in their respective careers.
Paterson is currently set to spend the rest of the season with Huddersfield due to the terms of his loan, and that means Brentford’s task to sign him will be complicated.
The Terriers also have first option to match any bid that Forest accept for the winger, and the Huddersfield Examiner suggests it will be tough for Brentford to get a deal over the line.