Openers Rahul and Vijay, who have one 50-plus partnership between them in the last four innings, are likely to be replaced by Agarwal and Hanuma Vihari at the top of the order.
Agarwal, who has amassed 3599 first-class runs at an average of 49.98, will become the 295th cricketer to represent India in Tests. The 27-year-old was drafted into the squad for India's home series against the Windies earlier this year, but did not feature in the playing XI, as Prithvi Shaw was selected ahead of him for the two Tests.
India name Playing XI for 3rd Test: Virat Kohli (C), Ajinkya Rahane (VC), Mayank Agarwal, Hanuma Vihari, Cheteshwar Pujara, Rohit Sharma, Rishabh Pant (WK), Ravindra Jadeja, Mohammed Shami, Ishant Sharma, Jasprit Bumrah #TeamIndia #AUSvIND pic.twitter.com/DImj8BVTj5
— BCCI (@BCCI) December 24, 2018
Vihari, who has been impressive with the bat in the middle order, is likely to be promoted to the opening slot alongside the debutant.
Rohit, who had to sit out in Perth after sustaining a lower-back injury in the first Test, has been brought back into the playing XI in place of one of the openers. The right-hander had contributed scores of 37 and 1 in India's 31-run win in Adelaide.
Jadeja, who was not picked for the second game due to a stiff shoulder, has also come in for Umesh Yadav. However, Ravichandran Ashwin, who was ruled out of the Perth Test due to an abdominal strain, has not recovered in time.
Snapshots from #TeamIndia's training session at the MCG 📸📸🇮🇳 #AUSvIND pic.twitter.com/kgnei1OsON
— BCCI (@BCCI) December 23, 2018
Pacers Ishant Sharma, Mohammed Shami and Jasprit Bumrah, who have 30 wickets between them in the series so far, have kept their place in the line-up. Hardik Pandya, who had been brought back to the squad for the remainder of the series after recovering from a back injury, misses out on the XI.
The Boxing Day Test between Australia and India will be played at the Melbourne Cricket Ground from 26 December.
India playing XI for the third Test: Virat Kohli (c), Ajinkya Rahane (vc), Mayank Agarwal, Hanuma Vihari, Cheteshwar Pujara, Rohit Sharma, Rishabh Pant (wk), Ravindra Jadeja, Mohammed Shami, Ishant Sharma, Jasprit Bumrah