According to the Daily Star, the 47-year-old now only speaks to his Italian-speaking staff.
A source close to the club said: "Conte these days only speaks to the close circle of coaching staff including his brother that he brought to the club with him.
"He does not speak to any of the English staff. There is virtually a total cut off at the training ground."
The Blues lost 1-0 to Manchester City on Sunday. Conte was criticised heavily for his defensive tactics, including three of his own players.
Giroud said: "Could we have been more ambitious? It is a good question. The coach made his tactics. We tried to respect that."
And Alonso added: "It's an attitude problem. We have to change the attitude. We don't have a problem with quality."