The Baggies have again achieved survival in the Premier League, but with Tony Pulis looking to kick on with some new signings at the end of the season, it seems that two Celtic stars are on his wish list, according to the Daily Record.
Defender Charlie Mulgrew and winger James Forrest have both had their problems with injuries over the years, but have been vital parts of Ronny Deila's squad at Celtic Park.
Now though, Mulgrew could leave at the end of the season, given that he's out of contract and can sign for another other club on a free transfer, making him a potentially shrewd signing.
The 30-year-old, who has 22 Scotland caps, actually turned out for West Brom's fierce rivals Wolverhampton Wanderers, but after an unsuccessful stint at Molineux from 2006 to 2008, Mulgrew moved back to Scotland with Aberdeen.
His fine form at Pittodrie handed him a return to former club Celtic, where he has proven his versatility by playing at centre back, left back and in defensive midfield - and that could be valuable to West Brom on a free transfer.
Mulgrew may be joined at The Hawthorns by Celtic and Scotland team-mate James Forrest, with the report suggesting that West Brom are also keen on the winger.
Forrest, 24, has come up through the ranks at Celtic but recently snubbed a new contract with the club, and he can become a free agent in January 2017.
Celtic may look to cash in before then though, and it's suggested that West Brom want to add pace out wide and see Forrest as a bargain option, given that Celtic may have to sell for less than £1m this summer.
Would you like to see West Brom sign Mulgrew and Forrest?