The Baggies have been chasing Hoefkens for a number of weeks and have failed with at least one bid as the Potters were unwilling to sell another defender before getting a replacement in.
Wright, predominantly a right-back, is now set to move to the Britannia Stadium on a six or 12-month loan deal so Hoefkens may be allowed to leave the club.
City have reportedly opened contract talks with the 28-year-old but it remains to be seen whether they will turn down an improved offer, with Albion lining up a £1million bid.
However, Tony Pulis is also short of experience in the left-back department and first team coach Mark O'Connor has hinted Wright could be used there, meaning Hoefkens may yet extend his deal and stay in the Potteries.
O'Connor told the club's official website: "Stephen is another very good player.
"He is like Andy Griffin, he can play in both full-back roles, is aggressive and can get up and down the pitch."
Meanwhile, Danny Higginbotham has also opened talks over a new deal.
City rejected an offer of around £2million for their captain last week and the 28-year-old has now urged the club to prove how much they value him by offering him an improved deal.
He told the Sentinel: "We are hopeful, my agent and myself, that there will be something on the table in the next week or so that reflects the ambition of the club and how much they value me."