Cresswell is currently on loan at Millwall but the Potters are now considering signing him in the final hours of the transfer window.
Stoke earlier agreed on a deal worth £20m to sell defender John Souttar to Leicester City and are in the market for a centre-back.
They are looking at several players but the Leeds defender has emerged as a big target for the club today.
It has been claimed that Stoke are seriously exploring a deal to take Creswell to the bet365 Stadium.
The centre-back has impressed in the Championship and has caught the eye of Stoke with his performances.
With Souttar gone, Stoke have the funds to do a deal and are now pushing to try and sign Cresswell.
Cresswell’s loan stint at Millwall needs to be terminated if Stoke can agree on terms with Leeds for the centre-back.