The Italian's team has slipped to six points behind joint leaders Manchester City and Manchester United, both on 19 points after seven games.
Now Conte looks likely to be without Alvaro Morata and N'Golo Kante until at least the middle of November.
The newspaper says Kante has been ruled out for the rest of the month meaning he'll miss this weekend's trip to Crystal Palace as well as further league games against Watford, Bournemouth and Everton.
Morata only arrived in England in July, becoming Chelsea's most expensive signing ever, but his importance to Conte's project has become apparent immediately: The 24-year-old Spaniard has already scored eight goals in 10 appearances.
The former Leicester man was substituted in the first-half of France's World Cup qualifier against Bulgaria with a hamstring injury.
However, the good news is as long as Kante doesn't suffer any setbacks during his recovery, the French global should be back in contention for the visit of Manchester United on November 5th.
The Spaniard picked up a hamstring injury in the loss against Manchester City last month and was sent home from worldwide duty after Spanish doctors claimed he could miss up to eight weeks out. Chelsea appeared to be in pole position to take Rose, who seems determined to burn all his bridges with Spurs, but he has all but declared that he wants to link up with Jose Mourinho and United, moving back to his more northerly roots than staying in London.
The couple tied the knot over the summer during a June wedding ceremony in Venice, a month before Morata moved from the Bernabeu to Stamford Bridge.