In the absence of Warner, who was recovering from a groin muscle tear, Australia's batting failed miserably in the first two matches.
The final call on who will play between Shardul and T Natarajan will be taken by the head coach Ravi Shastri, stand-in skipper Ajinkya Rahane and bowling coach Bharathi Arun after reaching Sydney.
Umesh ruled out of the remainder of Australia vs India series and is set to return to India; T Natarajan is the likely replacement.
The matches were due to take place on January 22 in Canberra, January 25 in Melbourne and January 28 in Hobart.
India bagged 30 points for their eight-wicket win. They are placed second with 390 points and a 72.2 percentage of points (PCT).
Rohit's entry certainly adds to the team's choices but whether it can help solve the opening conundrum is something that only time will tell.
Smith, who was named Test player of the decade this week, has managed just 10 runs in the first two matches, while Labuschagne could not capitalise on the starts with scores of 47, 6, 48 and 28 in the four innings so far.
Burns has been dropped after his scores of 8, 51*, 0 and 4 in the first two Tests and will Warner all set to make his return after having recovered from the groin injury he incurred during the ODI series against India.
With Shubman Gill showing calmness and maturity beyond his age in his debut Test, the team is likely to fit in Rohit either at the expense of Mayank Agarwal at the top or Hanuma Vihari in the middle-order.
Both Smith and Labuschagne have not been among runs with Smith aggregating just 10 across four innings at an abysmal average of 3.33 and Labuschagne doing slightly better but lower than his standards
India shrugged off the Adelaide Test humiliation to level the four-match series 1-1 with an eight wicket win in Melbourne inside four days.
Ajinkya Rahane-inspired India defeated Australia at the MCG by eight wickets to level the four-match series 1-1.
Cricket Australia had announced that the third Test will be played in Sydney as scheduled after days of speculation that it could be moved to Melbourne following a rise in Covid-19 cases
India coach Ravi Shastri on Tuesday told media that the team management will have a chat with him about how he feels before taking a call on his availability.
It took less than an entire four days for the same Indian team, who were without four of their main players - Kohli, Shami, Ishant Sharma and injured Umesh Yadav - to wrap up an epic comeback, one to be part of India's cricket folklore for ages to come.
India's fifth bowler, Ravindra Jadeja who played as an all-rounder came good after pacer Umesh Yadav limped off the field early in Australia's second innings on Monday following pain in his ankle.
The 58-year-old former India all-rounder compared Rahane to Kohli, saying that though both are good readers of the game they are different in nature.
Asked where he would place this week's MCG win, the India coach said this win deserves a place in the annals of cricket history.
Following the eight-wicket win, Virat Kohli took to Twitter to congratulate the Indian team and Ajinkya Rahane for his captaincy.
Rahane, who scored a brilliant century in the first innings to lead India's revival after they were reduced to 116/4, said going in with five bowlers worked well.
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