Stand-in captain Steve Smith confirmed out-of-sorts No.3 Marnus Labuschagne will hold his spot when Australia push for a 2-0 series win from Thursday.
Smith could not rule out spin-bowling allrounder Connolly, 21, earning a whirlwind Test debut on a Galle deck expected to turn plenty.
"It's possible, all options are on the table," stand-in captain Smith said from the team's beachside resort.
"We're not going to name the team just yet, we'll wait and see what it (the wicket) looks like again tomorrow."
Connolly, fellow allrounder Beau Webster and third front-line spinner Todd Murphy began Wednesday's final training session taking turns bowling on the centre wicket.
The trio are seemingly competing for two spots, with Connolly providing a valuable second left-arm off-spin option next to Matt Kuhnemann - the series opener's leading wicket-taker.
Connolly spent significant time batting in the nets, at one stage while Smith, vice-captain Travis Head, selector Tony Dodemaide and coach Andrew McDonald met to talk shop.
The Australian brains trust will leave it until the last minute before naming the bowling attack. (James Ross/AAP PHOTOS)
Webster can bowl right-arm off-spin but Smith favours Head as a part-timer; he took 4-10 in Galle in 2022 and was thrown the ball ahead of Webster in the first Test.
"He's done really well here before, presents that side spinning seam but Beau's also certainly another option," Smith said.
Connolly could come into the team for Webster if conditions point to favouring left-arm off-spin.
"(He's) another batter that bowls more than handy spin and spins the same way as Kuhnemann. We've got a few that go the same way as Nathan (Lyon) and Todd, (Murphy)" Smith said.
"We're going to leave it (the decision) until the last minute."
Smith would also not guarantee Murphy's place in the XI after middling match figures of 1-85 in the first Test.
"Everything's on the cards," Smith said.
"Todd, watching him bowl in the nets the other day after the first Test and before this one, he bowled beautifully.
"He's taken a couple of learnings out of the last game, which he can continue to take if selected."
Smith said Connolly's lack of first-class experience would not necessarily work against him after impressing at the team's preparation camp in the UAE.
The 21-year-old is a batter first and has not taken a wicket in his 16 first-class overs for Western Australia.
"It's entirely different, the way you bowl (in the subcontinent)," said Smith.
"He was pretty consistent when he was bowling in Dubai and in the nets here.
"That's kind of all you've got to do in these conditions, just try and bowl as many good balls in a good area and let the conditions take over."
Labuschagne was the sole specialist batter to miss out in Australia's rollicking first-Test win, caught behind on 20 as Smith, Usman Khawaja and Josh Inglis tonned up.
Marnus Labuschagne has been granted a reprieve and keeps his place in the team for the second Test. (Joel Carrett/AAP PHOTOS)
Legspinner Jeffrey Vandersay notably troubled Labuschagne before claiming his wicket, with the Queenslander averaging 31.6 since the start of 2023.
Labuschagne has made only one score above 100 in his last 49 Test innings but hit two valuable half-centuries in the tight MCG victory against India over the summer.
Eyebrows were raised when Labuschagne batted away from his fellow specialists at training on Tuesday, but the No.3's spot is not in doubt for the series finale.
"I can't see the top six changing, I daresay that'll be the same," said Smith.
"(Labuschagne) played nicely at the back end of the summer, he looked like he was putting the pressure on the bowlers a little bit more.
"The more difficult the wicket is in terms of how much it's spinning, the more aggressive you have to be with your batting and the more proactive you have to be.
"He understands that, he understands spin and angles as good as anyone. I don't think he's far away from a good score."
