The Portuguese winger has been absent recently with a hip injury, but Sir Alex says he and his coaching staff will assess Nani in training on Friday before making a decision on whether he will play at The Hawthorns or wait for Stoke City's visit to Old Trafford on Tuesday.
"We're looking at Nani as a possibility," the boss told reporters at Carrington on Friday. "We'll see how he is today, but he maybe has more chance of playing against Stoke."
Either way, Sir Alex will look to "freshen things up" against Roberto Di Matteo's side. "We may look to make one or two changes," confessed the boss, "as one or two looked a bit tired in the last few minutes against Birmingham.
"We expect a tough game on Saturday. West Brom have been a refreshing team this season - they play the right way and have a good threat. Their goal tally has been very good this season, particularly away from home. So we know it won't be easy."
United are still without Paul Scholes, but he could rejoin the first-team training squad next week. "He suffered a recurrence of a groin injury," explained Sir Alex. "So we told him to take a complete break and hopefully that will get it sorted. We hope to have him back in training next week."