Forest boss Stuart Pearce is desperate to bolster his defensive options due to injuries to a number of players and has lined up a move for full-back Hunt.
The likes of Kelvin Wilson, Jamaal Lascelles, Jack Hobbs, Eric Lichaj and Chris Cohen are all recovering from injuries and Pearce is looking to add to his squad with the new Championship season just over two weeks away.
Hunt, who joined Palace from Huddersfield last summer, has yet to play for Palace after breaking his ankle soon after arriving at Selhurst Park.
The 23-year-old enjoyed a spell on loan at Barnsley in the second half of last season, making 11 appearances in a bid to regain his full fitness.
Palace are happy to loan out Hunt again next season and Forest are expected to seal the signing of the right-back in the next 24 hours.