Conte has confirmed this week that he will leave his post with the Azzurri after Euro 2016 as he is keen to return to club management.
Goal understands Conte will sign a three-year deal with the Blues and has already told the club he wants to bring Vidal, Radja Nainggolan and Juan Cuadrado to Stamford Bridge.
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“I have always said if I go to war I would take Conte with me. We will see what happens," he told reporters.
The duo worked together at Juventus winning three Serie A titles after Vidal joined from Bayer Leverkusen before Conte’s departure in 2011.