The news that video footage is being studied to decide if Cheika came out with what he is alleged to have said comes a week after England head coach Eddie Jones apologised for a verbal obscenity of his own.
Cheika could be in trouble after being caught on camera using the alleged swear word and the word "cheats" during his side's 30-6 loss to England at Twickenham on Saturday.
A disciplinary officer's post-match report will inform both the Rugby Football Union and the Australian Rugby Union if any action is to be taken against the 50-year-old from Sydney.
The alleged incident came after a Michael Hooper try was disallowed and Cheika, who also became involved in a heated exchange with a fan during the match, said: "That's my own way of dealing with stuff. I like to get it out and get on with it."
If Cheika has a case to answer, he would have to appear in front of a disciplinary hearing before Australia's match against Scotland match on Saturday.
French vice-captain Yoann Maestri was fined 30,000 euros by a Six Nations disciplinary committee for a similar "cheats" comment he made following a match in March between France and Wales that ran for almost 100 minutes.