The Italian has worked with the centre-back during his time at Juve and the Italian national side.
And now, according to Gazzetta dello Sport, Conte wants to link up with 28-year-old Bonucci again when he takes over at Chelsea this summer.
The Italian manager has made defensive reinforcements a priority during his first transfer window at Stamford Bridge.
Current captain John Terry is expected to leave while fellow centre-back Kurt Zouma is a long-term absentee due a knee injury.
And, as a result, Conte is ready to break the bank to land Bonucci this summer.