In a week of turmoil at the club with the abject Champions League defeat against Roma on Tuesday, there are suggestions there is not a lot of love emanating from his dressing room either.
But Conte was perfectly candid about his relationship with the 19 other managers currently in the English top flight.
"Do I have any friends? Honestly, I think not now, no,” he said. “Before, I had a really good relationship with Claudio Ranieri and also now after the awards for the best coach and the best player at FIFA, we went for a dinner with our wives.
"But I think it’s very difficult to speak about ‘friendship’ with other coaches because then they become an opponent. You can have respect, respect for the job and the work, but to speak about friendship is very difficult.”
Certainly there is little love lost with Sunday’s opposite number Jose Mourinho returning to Stamford Bridge for the first time since claiming he would always be the “No1” at Chelsea until somebody surpasses his tally of three league titles.
Conte, though, was not about to be drawn into a bragging contest.
"That the club can be happy, the fans can be happy and the players can be happy with your work,” he said. “This must be our task. Then, if you are No4, No5, No6, this is not important. The most important thing is to have respect from your club, your fans and your players.”
Trouble is for Conte, after lifting the title just six months ago, that seems to be dissipating by the second.
Sources at the club are adamant that nothing should be read into Conte’s revelation that Roman Abramovich was down at the training ground on Sunday. His half-a-dozen or so visits to his empire are amiable enough affairs and it is more sinister if the Russian billionaire inexplicably seems to be keeping a distance.
More significant, though, was the heart-to-heart on Thursday in which Conte read the riot act to his squad following their performance in the second half against Roma in particular, although the Italian claims the process has taught him some new lessons about the character of the players in his dressing room.
"This season we are struggling,” said Conte. “We are struggling a lot because we are facing a lot of important problems. And to solve these problems is not simple.
"At these moments, though, you can see if you are winners or losers. It is very important, these moments. When the period is positive, it’s very simple for everyone to play well, to have great confidence.
"But in the times when you’re struggling, it’s important to show our character. To be strong and to face the problems in the right way.”