The Baggies are desperate for defensive reinforcement and are keen to sign the £4million-rated centre-back.
With Jonny Evans leaving the club, and the futures of Craig Dawson (who has slapped in a transfer request) and Ahmed Hegazi in serious doubt, West Brom are looking at new faces to rebuild the squad.
The 27-year-old is under contract at Swansea till 2021, but there is a strong interest in him from clubs like Leeds and Birmingham.