Returning to the bowling crease would mark the final stage of Green's carefully looked-after return to cricket after a spinal fusion operation in Christchurch.
Following the retirements of Chris Rogers, captain Michael Clarke and all-rounder Shane Watson, Smith will lead a team in transition into the three-match series which wraps up with cricket's first day-night Test at the Adelaide Oval.
Australia, on their first tour of Pakistan in 24 years, finished day three 205 behind but scored freely after resuming on five for no loss.
Khawaja and Smith steadied the ship batting through the second session.
Uncapped McSweeney to open with Khawaja in India series
West Indies' fearsome bowling attacks of old, Jayden Seales and Shamar Joseph tore through Australia on Wednesday
Images from Day 1 of the third Test between Australia and India in Brisbane on Saturday.
The entire Australian top-order that is feeling the "pressure" despite the series-levelling win in Adelaide
Mahmood has played two Tests, 9 ODIs and 18 T20s for England.
A heated exchanged between India captain Jasprit Bumrah and Australia opener Sam Konstas lit up an eventful Day 1 of the fifth and final Test.
'I like to think we're starting to move on from that, but there's definitely still that undertone ...'
Virat Kohli's conduct came under the microscope in the Boxing Day Test in Melbourne on Thursday after a clash of shoulders with teen debutant Sam Konstas, but the incident did little to knock the Australian wonder boy off his stride.
On Day 5 of the 3rd Test at the Gabba in Brisbane, Bumrah shook up Australia's top order early after lunch to carve his name in the annals of Indian cricket history.
Usman Khawaja along with three others was suspended for one Test during Australia's tour of India in 2013 for not submitting a 'homework' assigned by the coach.
Skipper Pat Cummins, who missed the tour of Sri Lanka due to the birth of his second child in February and was also ruled out of the Champions Trophy campaign with an ankle injury, will take the reins against South Africa.
With Green out with injury, Bancroft's chances have brightened.
His loss for even part of the series would be a huge blow to a team already missing so much batting experience because of the Cape Town ball-tampering scandal.
Bumrah, who claimed an eight-wicket match haul in India's 295-run win in the series opener, showed signs of discomfort while bowling the 81st over of Australia's innings.
Hazlewood was initially named in the squad for South Africa, will also return home following the Test series. Xavier Bartlett has been drafted in as his replacement.
Out-of-favour opener Usman Khawaja, who clashed with Justin Langer during Australia's tour of UAE in 2018, has backed the embattled coach to continue in the position through the Ashes and urged the payers to stop undermining him.
'Have a look where Virat walks. Virat's walked one whole pitch over to his right and instigated that confrontation. No doubt in my mind whatsoever.'
Steve Smith's magnificent 71 guided Australia to 221 for seven at stumps on Day 3 of the second Test against the West Indies in Grenada on Saturday, helping the tourists to build a commanding 254-run lead despite late wickets and persistent rain interruptions.
Alex Carey scored 63 and Beau Webster 60 as Australia were bowled out for 286. West Indies pacer Alzarri Joseph took 4 wickets for 61 runs on Day 1 of the second Test.
'The prospect of Konstas facing Jofra Archer with the first ball of the Ashes on November 21 -- potentially delivered at 155km/h -- doesn't feel like a fair fight.'
Gillespie said that he feels that either one of Labuschagne or Usman Khawaja, the 38-year-old who failed to touch double-digits in both WTC final innings, will miss out on West Indies tour, which comprises three Tests, starting June 25.
The West Indies produced another dominant day with the ball against Australia and then survived a tense final hour Saturday to take the honours after the first day of the day-night third Test.
Glenn McGrath said his prediction this time is based on how England were held to a 2-2 series draw by India in the recent Anderson-Tendulkar Trophy five-Test series.
Australia, who have already secured their place in the final of the World Test Championship against South Africa, won the opening Test, also in Galle, by an innings and 242 runs.
'I was born in Islamabad but my parents are from Karachi, so this one meant a lot'
In-form batsman Usman Khawaja has been selected to play his first one-day international in three years when Australia meet New Zealand in the second match of their series in Wellington on Saturday.
Australia opener Usman Khawaja has vented his frustration after the team lost 10 World Test Championship (WTC) points for slow over-rates.
Images from Day 3 of the fifth Test between Australia and India at the Sydney Cricket Ground on Sunday.
Beau Webster believes playing against India pacer Jasprit Bumrah will be an enormous challenge for the Australian pacers on the seamer-friendly SCG pitch.
The debate over the vacant slot at the top of the Australia batting order continues to captivate the nation's sports media a month before the opening clash in a blockbuster five-Test series against India.
South Africa's dream start to the World Test Championship final quickly turned into a nightmare at Lord's, as their batters failed to back up Kagiso Rabada's five-wicket masterclass.
Top order batsman Usman Khawaja has been omitted from Australia's annual list of 20 elite, contracted players in 2020 after falling out of favour with selectors midway through last year's Ashes. The 33-year-old lefthander has not played for the Test side since being dropped after the third match against England in Leeds last August.
'You hear things like 'the players are playing afraid' or whatnot, but that's what happens when you drop players all the time. We've been doing that a fair bit lately'
Change will be a key theme for both the West Indies and Australia in their upcoming three-Test series in the Caribbean with the visitors set to field a remodelled batting line-up and the hosts being led out for the first time by Roston Chase.
Having recovered from a hamstring strain, Usman Khawaja celebrated his recall with a glittering 144, with Queensland team mate Joe Burns making 128 in front of a festive Melbourne Cricket Ground crowd to drive Australia to 345-3 at stumps.
Khawaja and Stoinis were included despite losing their national contracts after falling out of favour with selectors over the home summer.