Recent reports in Italy have linked Juventus boss Max Allegri and Napoli coach Maurizio Sarri with the Chelsea job, and Conte realises that being a Premier League manager does not come with a lot of job security.
Central defender Eric Bailly is another on the sidelines and his return to fitness from an ankle issue holds the key to whether Mourinho will allow 20-year-old Axel Tuanzebe to leave on loan in this transfer window.
New signing Ross Barkley is working his way back to fitness and could make his Chelsea debut in the FA Cup third-round replay against Norwich in midweek.
Antonio Conte has been in a feisty mood lately - or maybe it's just his constantly improving English? - ready to fight anyone and everyone foolish enough to cross his path. One day it's Mourinho, another day it's Wenger.
"No, I think when a person insults another you can expect a response", he said.
Conte's position has been the subject of speculation regarding a rumoured frustration over transfers.
I repeat, I have a lot of experience to deal with this type of situation.
Conte has continued to pick Morata over Michy Batshuayi throughout the Spaniard's cold streak, but he dismissed the suggestion that there is a lack of serious competition for places up front in Chelsea's squad.
Having spent a good portion of last season exchanging abuse via the media, the war of words reared its ugly head again at the turn of the year, when Mourinho said: "You don't have to behave like a crazy guy on the touchline".
The 47-year-old won two La Liga titles and the Champions League in his three seasons in charge at the Nou Camp before quitting last year.
Jesse Lingard was one of our picks to bring in a couple of Gameweeks ago and now it's time to go one step further and hand the United man the captain's armband.
Conte said: "I said 'hello'".
"I'm happy. I'm enjoying my period here". Responding to the claims, Conte mentioned that he "wasn't mocking anyone".
"He knows very well my admiration for him. It was a technical substitution".
Asked if more could be read into their conversation, Conte added: "No, not other situation or other conversation".
Now let's take a look at what Chelsea fans made of his first training session alongside the club's stars...
"We are talking about a top player in a moment when you can buy him with a price not so high".
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