"If the conditions are not met the penalties will be invoked after any appeals process is exhausted," the ATP confirmed.
The action comes after Kyrgios made headlines around the world for his offensive "Kokkinakis banged your girlfriend" remark concerning Wawrinka's reported girlfriend, teenage tennis star Donna Vekic, during a match against the Swiss star in Montreal 10 days ago.
He was fined US$10,000 for the incident at the time.
The ATP said it analysed information gathered from various sources on-site and looked at a submission on behalf of the player.
"This incident was egregious and reflected poorly on our sport," Bradshaw said.
"Nick has expressed regret and the best result would be that he learns a lesson from this incident and that he understands he is responsible to the tour and to fellow players for both his actions and his words.
"It is with these factors in mind I feel he should have the opportunity to 'earn' his way out of additional sanctions."
Kyrgios insisted last week he'd made appropriate apologies following his outburst, despite Wawrinka saying that was not the case.
"I have been reading reports that I did not apologise for my comments, which is untrue," he said in a statement posted on Facebook.
That incident followed a controversial Wimbledon campaign by Kyrgios. Despite playing some sublime tennis to reach the last 16, much of the focus centred on his on-court conduct after a series of clashes with umpires and officials.
Notably, he was forced to defend himself in the first round after yelling out "dirty scum" and accusing umpire Ali Nili of thinking he was "top dog".
- AAP
