Morrison, who has scored five goals from 23 Premier League appearances this season, picked up an ankle injury this week and manager Tony Pulis revealed the midfielder may not be available for selection.
He said: "James Morrison has hurt his ankle this week so we aren't sure if he will be available for the game."
The Baggies could also be without Matt Phillips for a fourth consecutive game as the forward continues to recover from a hamstring complaint.
The 26-year-old Scotland international has been a revelation since joining last summer, having scored four times from 24 league outings, and the boss admits his impact has been missed.
He added: "You need good balance to win games. With Phillips in the team we have good balance and that's what we've missed."
Pulis is expected to recall striker Salomon Rondon to the starting 11, having dropped the Venezuelan to the bench for the 3-0 defeat to Everton last time out.
Wales international Hal Robson-Kanu will drop to the bench whilst Jake Livermore, who was named in England's squad on Thursday, will line-up in the centre of midfield.