Cresswell is currently enjoying a three-month loan at Bramall Lane and the versatile forward has scored once in five appearances.
He has recently returned to the Blades team after a rib injury and is now set to stay with the Championship club in the New Year.
Blades boss Kevin Blackwell confirmed that a deal is in place for the former Sheffield Wednesday man to finalise the move when the transfer window reopens.
"Everything looks like it's been done with Cressy," Blackwell told the Sheffield Star.
"We've been talking with Stoke for a while and we've come to an arrangement about how much we'll be paying.
"Cressy is a brave lad and a very experienced player who we were pleased to get in the first place. He's seen everything in the game and is very valuable to us."