Mawson will miss the start of the new Premier League season as the centre back recovers from a knee injury.
The 24-year-old has been ruled out of at least three league matches as he battles for fitness after having surgery in May.
“He won't be ready. We will be waiting between two and three weeks for him to start working with us," Jokanovic told the London Evening Standard. “I don't expect he can help us before September."