Connolly was spotted leaving Kingsmead in a van after training on Thursday (Friday AEDT) afternoon on the eve of the first Test against South Africa, while the rest of the side moved back to the Durban team hotel on a bus.
It is understood the 23-year-old has a head cold and Australia opted for caution after he trained normally through the afternoon session.
Still, it comes at an interesting time for the West Australian ahead of the first Test.
Australia are already without their regular No.5 in Cameron Green due to an abdominal strain, while Josh Inglis is back in Perth with a fractured finger.
The tourists will wait to see how dry the pitch is on Friday before announcing their side at the toss, with Connolly and Nic Maddinson in contention to come in for Green.
Connolly has not played a Test since his debut against Sri Lanka last February, while Maddinson's last appearance came way back in December 2016.
Both could play if the wicket is particularly dry, given Maddinson is a noted player of spin and Connolly offers left-arm tweakers.
One potential option would be for that to come at the expense of Beau Webster, who batted at No.7 in the recent Test series against Bangladesh.
South Africa have already confirmed they will play two spinners in Keshav Maharaj and Simon Harmer, in a clear sign of how they believe the wicket will play.
"Everyone brings something a little bit different to it, and it's just trying to work out what we think the best combo is," Australia captain Pat Cummins said.
Green is a chance to return for Australia in the second Test, while Inglis is recovering well and is expected to fly back to South Africa before the series ends.
Australia are also confident Marnus Labuschagne has shown signs he can return to form at No.3, after a century in their warm-up game last weekend.
The 32-year-old has not reached three figures in any of his past 39 completed Test innings, and was briefly dropped for last year's tour of West Indies before fighting back.
"He doesn't need to go searching for something that he doesn't already have," Cummins said.
"I think it's him finding his way back to when he was at his best, and we've seen that in the last six months.
"I know a lot of it hasn't translated into Test runs, but we love what he's bringing, we love his approach.
"He's hitting the ball beautifully in the nets, I know it doesn't guarantee success out in the field, but we think he's really well placed."
Australia have spoken about the need to potentially play this Test at a different tempo to many recent ones, which have been dubbed as "fast-forward cricket".
"We've got to get a little bit better, and we can get a bit better at, getting to the grind," Cummins said.
"It might not be the glamorous stuff, but it's that grinding out a session, going for two runs an over, not these major falls or not these whirlwind innings at the time.
"We haven't played too many of those Test matches in the last few years, particularly in Australia, they've been quite fast-paced.
"A lot of our success has come off these big moments, with a Travis Head hundred or Starcy running through the top order."
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