India won the second Test at MCG by 8 wickets to equal the series 1-1.
The left-arm seamer from Tamil Nadu already made his ODI and T20I debuts during the limited-overs leg of India's ongoing tour of Australia.
As per reports of the Times of India, 29-year-old Natarajan, who took two for 70 on his ODI debut and then scalped six wickets in the three-match T20 International series at an economy rate of 6.91, is set to replace fast bowler Umesh Yadav, who suffered a calf injury and could bowl only 3.3 overs in the second innings of the second Test at the MCG.
"The selectors had added Shardul Thakur (Mumbai paceman) as a replacement for Mohammed Shami (out with a fractured forearm), and there is Navdeep Saini too, but it's very much likely that Natarajan would be preferred given that he brings variation to the attack.
Also, As Mitchell Starc does for Nathan Lyon, he would create footmarks which spinners Ravichandran Ashwin and Ravindra Jadeja can exploit," a source said on Sunday.
Also, possible inclusion is that of KL Rahul, in place of Hanuma Vihari, who has failed to impress the two Tests that he has played so far.
The third Test between Australia and India begins in Sydney from January 7 onwards.
(Times of India sources)