Kohli was captured pics of raising his middle finger as India fought to contain Ricky Ponting and Michael Clarke during the series of their 288-run partnership, the highest fourth-wicket partnership ever created against India in Test cricket.
A similar happening was seen in the English Premier League when Liverpool's Luis Suarez was restricted for a match after indecently gesturing at a section of Fulham's fans.
Last month, Kohli had been penalized for showing dissent at an umpire's decision at the time of the third ODI against West Indies in Ahmedabad. He had stood his ground for a significant time after being given out lbw, and later pleaded guilty to a Level 1 offence while agreeing to the proposed sanction from the match referee David Boon.
On the other hand, Kohli in his twitter account wrote, "I agree cricketers don't have to retaliate. What when the crowd says the worst things about your mother and sister. The worst I've heard."
England batsman Kevin Pietersen replied to his tweet, "ha ha ha ha ha!!! Welcome to Australia buddy!!"
If Kohli is identified guilty, he could face a minimum penalty of having half of his match fee docked or a maximum penalty of a one-Test suspension.
However, so far the on-field umpires have not raised the issue with the match referee Ranjan Madugalle.