The 33-year-old left-back is being targeted to add more experience and competition to Wolves’ squad, and could follow Matt Doherty through the door with talks under way.
Cresswell is currently with West Ham on their pre-season tour of Australia, but did not play in their 3-2 win over Spurs on Tuesday.
If Wolves manage to complete the transfer, it could open the door for Rayan Ait-Nouri to leave on loan and could see Ryan Giles sold, with several clubs chasing his signature.
As a result, it would leave Cresswell and Hugo Bueno to battle for the left-back spot.
Wolves are also still in talks for Borussia Monchengladbach centre-back Nico Elvedi and Bristol City midfielder Alex Scott.