Bannan is expected to leave Selhurst Park on deadline day and Leeds and Forest have both been tracking his availability for some time.
The Scotland international has fallen out of favour under Alan Pardew's stewardship, with the side making a number of additions this window, and he is set to leave in search of first-team football.
Bannan has made 12 appearances for the Eagles so far this season and has never been able to show his top form.
What is the impact for Palace?
The loss of Bannan is unlikely to be detrimental to Palace's chances of staying in the Premier League. Although the attacking midfielder is unquestionably technically gifted, his lack of physicality is an obvious weakness and his form this campaign has not been good enough.
The 25-year-old is also unlikely to break into the team, with Palace's other options in his position looking like stronger players, and a move could be best for both player and club.
If he does switch to Forest or Leeds his transfer will be a loan one, because neither side are able to make permanent deals as they are working under a transfer embargo.