"The medical team will be doing everything possible to get him fit and available for selection ahead of the first test ... we expect to have a clearer picture of his progress later in the week," Kountouris added.
Watson suffered the injury while bowling in the final one-day match against India on November 2 in Bangalore.
His long injury history raises concerns the No. 3 batsman could be ruled out of the England opener or at least restricted to only batting in the Gabba match. He is Australia's fourth seam bowler.
The former test vice-captain will miss New South Wales's domestic match with Queensland starting next Wednesday, which would mean he'll go into the Ashes series without a recent first-class match.
If Watson is fit to take his part, it would appear Australia's only vacancy will be the No. 6 batting position, with George Bailey the leading contender.