According to the report, match referees Mike Procter and Jeff Crowe have asked BCCI to reign in the temperamental off-spinner.
"We are aware of Harbhajan Singh's comments and are in dialogue with the two boards (Australia and India)," the newspaper quoted an ICC spokesman as saying.
Harbhajan could be charged with unbecoming conduct, which carries penalties, including suspension, the report added.
The ICC's reported investigation comes after the BCCI had asked Harbhajan not to speak to the media on Australian tour.
Albeit Sydney Morning Herald quotted Harbhajan as calling Hayden "a liar" and Adam Gilchrist "no saint", the off-spinner had denied these reports immediately.
"Don't talk about Hayden's credibility, he is a big liar. Gilchrist is also not a saint. He, of course, pretends to be a saint - someone who doesn't say an offensive word on the field. But this is completely wrong. There are times when he doesn't let an opportunity go to waste. The whole world knows how the Australians target individual players to break their confidence", the daily had quoted Harbhajan as saying.
"Yes, we received a mail from Cricket Australia about Harbhajan Singh. He has been told not to talk to the media on the Australian tour. He has to accept our directive," BCCI secretary Niranjan Shah said on Sunday.