According to Telegraph journalist John Percy, a deal could be completed as soon as this weekend - with the Baggies ready to tie up their third transfer of the season, following the arrival of goalkeeper Sam Johnstone from Manchester United.
Having lost Jonny Evans to Leicester City in a cut-price £3.5m deal earlier this summer, West Brom appear to have identified Kyle Bartley as the man to replace him in the heart of their defence.
The 27-year-old only played 234 minutes of Premier League football last season, and was a fringe player during his time in south Wales - having only made 36 appearances since his arrival at the club in 2012.
Despite his limited game time in the Premier League, he impressed Birmingham City and Leeds United fans during loan spells with those clubs in the Championship.
It remains unclear as to whether or not he will be a first-choice defender for West Brom, given their ambition to return to the Premier League and his lack of experience in both achieving promotion to the Premier League and also in playing at such a level.
Meanwhile, West Brom have invited Kieran Richardson and Martin Cranie to train with them this summer, as the duo look to find a new club this summer. Any potential for the duo to sign for West Brom this summer has been ruled out.