The 32-year-old, who sustained a hamstring injury in the final match of the recent one-day tour of India, came through a light training session in Brisbane on Friday without any problems.
Watson's fitness to bowl could well have ramifications for the make-up of the Australia team for the first test at the Gabba as the hosts look to make a good start to their quest to wrest back the Ashes back from the tourists.
"My hamstring's progressing well, so far I haven't had any hiccups, it was only a minor one so hopefully it continues to progress the way it is and I'll be hopefully fit and fine for that first test," Watson told Foxsports TV.
"The bowling just depends on how I continue to progress leading into that first test.
"It's a matter of striking the balance between pushing it to see exactly where it's at without pushing it over the edge, which might mean I might miss as just a batsmen alone.
"If everything continues to go the way it is, then we potentially might start bowling at the start of the week but it depends on how it does progress."
Australia batting coach Michael Di Venuto was less equivocal about Watson's chances of batting in Brisbane, saying the 32-year-old was hitting the ball in the nets as well as he had in India.
"Batting is not going to be an issue. He is pretty confident where he is at the moment," he told reporters in Brisbane.
"As long as he can move and run around, he will be good to go for the first test.
"He is a world-class batsman," Di Venuto added. "If we have to, we will just use him as that.
"We have options to go whatever way we want, if we want to use a spinner or four quicks."
If Watson is not fit to bowl, fellow all-rounder James Faulkner could retain his place in the side after making his debut in the final test of the first Ashes series of the year, which England won 3-0.
Australia are trying to avoid a fourth straight Ashes series defeat over the next two months. The first test starts next Thursday.
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