Goal understands that Conte has already visited Chelsea’s training ground and is close to agreeing a three-year contract worth £6.5 million per year.
The 46-year-old is also expected to inform Chelsea that Roma midfielder Radja Nainggolan and Bayern Munich’s Arturo Vidal are his two priority transfer targets this summer.
Conte is set to move to Stamford Bridge following Italy’s Euro 2016 campaign, and Vialli has backed the former Juve boss to succeed in the Premier League.
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“In Italy they call him the Italian Mourinho – he has the same kind of personality,” Vialli told BT Sport.
“His teams play in a very humble, with humility and a lot of pride. Tactically they are always well prepared when they go out on the pitch.
“He is a winner as well. He won three consecutive titles in Serie A and I think if he signs the contract he will be a great choice.
“I think he’ll adapt. The key in the Premier league is to defend well and be solid at the back. Whatever happens going forward it’s a plus.
“An Italian manager might have a few faults but they’re capable of organising a side better than anyone else.”