Antonio Conte took charge of the first pre-season training session on Monday amid intense speculation about his future.
Chelsea were expected to have named a new head coach by now, but Conte remains at the helm after refusing to quit.
Conte was at Cobham on Saturday as some of the Blues squad returned from holiday to undergo fitness and medical tests.
The Italian was snapped in training by Chelsea TV greeting his players as they arrived for what ESPN called a double session.
Pedro, Cesc Fabregas, Marcos Alonso and Alvaro Morata were not involved in the World Cup with their international sides and reported for duty over the weekend.
Conte was not involved in the medical checks on Saturday, but instead attended meetings at Chelsea's training base.
The Guardian claim Conte oversaw the first proper pre-season session on Monday and will continue on as 'business as usual' until he is told otherwise.
Chelsea will need to sack Conte if they want the Italian to leave the club, but there is a reluctance to pay out the £9million compensation fee Conte would then be due.
The Blues are in talks with Napoli to bring Maurizio Sarri to Stamford Bridge, but the Serie A is refusing to let the coach leave without a fight.
Napoli want a healthy fee for Sarri, but have already replaced the Italian with Carlo Ancellotti.
The appointment of Ancellotti does not affect Napoli's hold over Sarri and Chelsea fans may well be made wait even longer for the club to make any official announcement about the future.
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