The rift has become more intense as Chelsea have failed to match their performances from last season, and Conte's tenure is looking increasingly in doubt after the Blues suffered their latest defeat to top-four contenders Tottenham Hotspur on Sunday.
"I would be surprised to see Conte at Chelsea next season because I think he is nearly looking forward to leaving, and I also think that Chelsea want to change, they want something new, maybe a manager who is more of a corporate man - people have been talking about Luis Enrique".
Chelsea have won 14 trophies since Roman Abramovich arrived at the club in 2004, but they have gone through 11 managers in that time.
The 46 percent increase in revenues - to June 30, 2017 - was largely due to the new Premier League TV deal and Spurs' participation in the Champions League, which they look likely to secure again next season.
"We deserve to be there".
"I don't know, you have to ask the club, not me".
There is a feeling in the camp the former Real Madrid man does not make football his priority - a big no-no for Conte who claims he works 24 hours a day.
"This is our task. He didn't play [for England] and he came back to training with a big willingness to show his quality and I think he is ready to finish this season strong".
Sources close to the club expect owner Abramovich will take a hands on role this summer to try to ensure Chelsea do not fall further behind their rivals. "But I repeat, I am not anxious about this".
I think that the players are giving everything this season. "We've thought it for six or seven months". I think if we are in this position, we are deserving of this position. "It's such that when you have a season slightly worse than before, you go".
The Italian has been linked with the Stamford Bridge exit following a disappointing Premier League title defence and rumours that he is unsettled in London.