The midfielder spent the latter half of the season on loan at Shrewsbury and has impressed with his performances in the third tier.
His showings at Shrewsbury have led to interest from several clubs in the Championship who have their eyes on him.
Newly-promoted Premier League outfit Luton Town have tracked Phillips and even Coventry City have been keeping tabs on the player, but they are keener on a loan move.
But it has been claimed that Stoke are the ones who are pushing to take the Palace midfielder to the bet365 Stadium.
Alex Neil has been left impressed with what he saw from Phillips in the third tier of English football and wants to sign him.
Stoke are looking at a permanent deal and are expected to table an offer to sign the Crystal Palace star this summer.
He will have a year left on his contract at Crystal Palace and is not expected to be part of their plans next season.
