The 21-year-old is understood to have already been fined over his comments about China on social media while the club were on pre-season tour in Beijing.
Kenedy was booed when he came on as a second half substitute against Arsenal in the Chinese capital on Saturday.
Both Chelsea and Kenedy have since released a statement issuing an apology, but the consequences for the Brazilian aren't likely to end there.
He faced an uncertain future at the club anyway having failed to impress since joining from Fluminense for £6.3m in 2015.
Kenedy has made just 22 appearances for the club in that time, just two of which have been under Conte.
A season-long loan at Watford last term was ended prematurely in January after playing just one game, with sources at the Premier League club suggesting he had an attitude problem.
In Pictures | Arsenal vs Chelsea | 22/07/2017
Chelsea could loan him out again in order for him to get more experience, but Conte will not have taken kindly to this episode.
When asked by Standard Sport today if he had spoken to Kenedy about the incident, Conte said: "About Kenedy, he understood his mistake and he is sorry for this for sure."
