Chelsea's first pre-season game is in Australia, against Perth Glory on 23 July.
The Italian is widely expected to be replaced by former Napoli manager Maurizio Sarri but the Premier League winning coach as Conte wore a tired look at the club's Cobham training base.
While Moses was absent, Alvaro Morata, Ross Barkley, Pedro, Marcos Alonso and Danny Drinkwater were all present for the training session.
Chelsea embarked upon this summer in the knowledge that big decisions would have to be made in order to return to contention at the top of the Premier League next season, while key players Eden Hazard and Thibaut Courtois both publicly challenged the club to show more ambition in the transfer market.
Meanwhile, the west London giants have begun pre-season training without the involvement of current boss Antonio Conte and this appears to give a clear indication that the 48-year-old should end his association with the club in the coming days.
England fans slammed by police as 'disgraceful' after win
Czechoslovakia and Yugoslavia advanced to the semi-finals in 1962 without a player aged 26 or over scoring for them. Millwall fans are collecting for the London Ambulance Service after a vehicle was damaged by people dancing on it.