Brunt has been sidelined with a calf injury throughout pre-season training, and although Clarke insists that he is not ruling out Brunt for the start of the season, he will not risk the Northern Ireland international's fitness.
Clarke told the Express & Star: "He has still got two weeks to get ready. He watched our friendly on Saturday but he wasn't ready to play.
"I'm hopeful we will join training some time this week."
West Bromwich Albion begin their Premier League campaign against Liverpool.