Irvine's players returned for training this week, but Morrison and Brunt were not among them after undergoing procedures on niggling injuries in the off-season.
Scotland international Morrison had been troubled by a knee problem, while Brunt had surgery to correct a groin strain.
Despite missing training, Irvine anticipates the pair to return in plenty of time for the new Premier League season, which gets under way on August 16.
"James and Chris have had small operations," he told West Brom's official website.
"James could well be training with us properly before we go on pre-season tour to America [later this month].
"We definitely expect him to be in full training in America.
"Chris' recovery will take slightly longer but we're hopeful he will be available for the Nottingham Forest game [on August 2] and back in good time for the start of the season."
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