Both are yet to feature for the Baggies in pre-season, with McAuley struggling with a thigh injury he picked-up on international duty, while Morrison has failed to shake-off a knee problem.
Morrison’s build-up to the campaign has been further hampered by him missing the recent Asia Trophy following the death of a close friend.
West Brom begin the new season against Bournemouth on August 12 and Pulis admits he is unsure if two of his traditional stalwarts will be fit to face the Cherries.
“Moz has missed out as well as McAuley,” he said. “They are the two we’ve got problems and issues with.
“By the time the season starts they’ll be closer. Whether they’ll be able to start we’re not sure. We’re hoping by the time the season starts they will be around about fit.”