Manager Darren Moore has already seen key defender Jonny Evans move to Leicester City this summer and has also lost Gareth McAuley after his contract expired, leaving few remaining defensive options.
According to Football Insider, West Brom are keen to improve their squad by signing Hudderfield's Hefele and have reportedly already enquired about the player's availability.
Hefele did not have much of an impact for the Terriers' last season, making only six appearances, with only two of those in the league.
The German was pivotal in helping Huddersfield get to the Premier League for the first time in the club's history by playing in 37 league matches, giving him plenty of experience in the Championship.
Hefele is reportedly approaching the last year in his contract and therefore may have the opportunity to leave the Yorkshire side in a bid to get more first team football.
He will likely play alongside new Baggies signing Kyle Bartley, who has recently joined from Swansea City.
With two defenders having already left the club, and Craig Dawson reportedly handing in a transfer request, the Championship side will have to be busy over the summer to ensure they are defensively ready for the new season.
Baggies fans will have high expectations of their manager, Darren Moore, after he helped guide West Brom to an undefeated streak in April last season, but sadly couldn't save them from relegation.