The shot stopper has been in limbo for several years, as he has been unable to get the move back to the Premier League he so desired.
No club has come close to matching what Stoke want for Butland.
Per The Telegraph, Palace will make an attempt to sign him in the last hours of the window.
Butland only has eight months left on his Stoke contract, which means they will be more inclined to sell him for a modest fee.
The former England keeper knows he must play top flight football to have any chance of being on the plane for Euro 2020 next summer.
Now Palace boss Roy Hodgson may be offering him a lifeline, if the move goes through.