Conte is still under contract at the Stamford Bridge outfit but is expected to leave the Premier Leave side as soon as Maurizio Sarri is finally named as new manager.
Moses will, however, hope to be part of the squad when Chelsea kick-start their pre-season with a friendly against Perth Glory on July 23 before entering the International Champions Cup at the end of the month.
But a contractual dispute with Napoli has prevented Chelsea from snapping Sarri up, leaving Conte at the helm after he regularly challenged the hierarchy's authority with comments about their transfer policy in the most recent campaign.
Chelsea finished the season disappointingly after coming fifth in the Premier League, missing out on a Champions League spot in the process.
Conte was not involved in any of the sessions on Saturday, but sources told ESPN FC that he intends to begin his own preseason programme with the squad on Monday unless he is sacked before then.
Antonio Conte remains in charge at Chelsea and is beginning the club's pre-season preparations today as senior players returned to the training ground over the weekend.
Numbers were diminished due to several players' involvement in Russian Federation, but those who didn't feature in Russian Federation were put through their paces with fitness and stretching exercises.
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.