The 29-year-old left Norwich on a free after his contract with the Championship side expired at the end of last season.
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Forest have been on the lookout for a new back-up goalkeeper following the departures of Matt Turner and Wayne Hennessey.
According to transfer guru Fabrizio Romano, Gunn will now join Nuno Espirito Santo’s side ahead of the upcoming 2025-26 season.
Gunn will likely come in as second choice behind Matz Sels, who kept an impressive 15 clean sheets across his 42 games last season.