Signing a left wing-back is high on Conte's wish list and Sandro has emerged as one of his main targets to provide competition for Marcos Alonso.
Last week Juventus general manager Giuseppe Marotta confirmed Chelsea made a "very big" bid for Sandro and stressed they were reluctant to sell.
But Italian outlet Calciomercato claim Chelsea will up their offer to £61.7million (70m euros).
Chelsea are prepared to offer Sandro a five-year contract worth more than £6m-a-year.
The report says Juventus are hoping to convince Sandro to stay in Italy and are looking at giving him a new contract on improved terms.
Funny how a top european club like juventus can't keep one of their stars away from the premier league. Crazy money for a defender though.
I don't remember juve's owners being desperate to sell or cash strapped so no reason to sell.
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It is good deal though, £61.7m for Sandro. I would sell it.
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Dopo aver venduto Bonucci non possiamo vendere anche Alex Sandro! 😞
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