The Italian gaffer was at Cobham on Saturday as some of the Blues squad returned from holiday to undergo fitness and medical tests.
Ross Barkley, Pedro, Cesc Fabregas, Tiemoue Bakayoko Marcos Alonso and David Luiz were among the big names to have returned. Maurizio Sarri was said to have been lined up to take over at Stamford Bridge and it appeared to be a matter of time before a deal was confirmed when Napoli sacked him in May for taking too long to decide on his future.
Napoli president Aurelio De Laurentiis is waiting for an improved offer from Chelsea and Sarri is not in London, as he waits for the go-ahead.More news: Amesbury nerve agent victim Dawn Sturgess sadly passes away in hospital
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But one factor that is blocking Chelsea from sacking Conte this summer is the fact that they would have to pay him £9 million as compensation with his release clause for one more year.
Conte is still now in charge, but Maurizio Sarri is expecting to be cleared to replace him as manager of Chelsea at the start of next week.
The prolonged uncertainty surrounding Conte and Sarri has had a paralysing effect on Chelsea's transfer plans in a window already complicated by the World Cup and compressed by the Premier League's earlier deadline, set for August 9.
CSKA Moscow midfielder and Russia World Cup star Aleksandr Golovin looks very likely to become the club's first addition of the summer for a fee of around £27m ($35.7m), with Juventus's Daniele Rugani having also had talks over a move.