Froome has been subjected to sustained scrutiny since his Tour win in 2013, with some sceptics using power data to justify their case against him.
The 30-year-old Briton has always insisted he is a clean rider.
"We think someone has hacked into training data and got Chris's files," said Team Sky boss Sir Dave Brailsford.
"We've got some legal guys on the case. I would never mention a name but ethically and morally if you are going to accuse someone of doping, then don't cheat."
Froome said critics on social media who try to interpret power data are "clowns", adding that it means nothing without context. He has also said he is prepared to be a spokesman for drug-free sport.
With Froome leading this year's Tour by 12 seconds going into Tuesday's 167km 10th stage, Brailsford says he is braced for more questions over doping.
"It's part of the game, isn't it?" he said. "If he does well [on Tuesday], the rest of the Tour it's 'how do you know he's not doping?'
"The question of how to prove a negative is always going to be a difficult one.
"I used to worry about it a lot more, but I don't any more. It's part of the game. Just try to be honest, tell the truth, be open."
Team Sky believe their computers have been hacked by critics convinced Tour de France leader Chris Froome is using performance-enhancing drugs.