The 32-year-old proved to be a key figure at Selhurst Park when he joined from Southampton, initially on loan, in 2013, but his chances have dwindled over the last 12 months.
Indeed, Puncheon was restricted to just 10 Premier League outings in 2017-18 and he is yet to turn out for the Eagles in the league this season.
He was linked with Middlesbrough over the summer but a switch to the Championship promotion hopefuls failed to materialise.
Reports claim he could still be handed the chance to leave Selhurst Park this term, although he will need to wait until January, as Forest are keen on his services.
It's understood that Forest are only interested in bringing in the winger on loan with a view to a permanent deal at the end of the campaign.