Conte is widely expected to be named as the next Chelsea boss, and he is already making plans for when he takes over at Stamford Bridge.
The Italian is likely to be backed with funds in the next transfer window, and Stones is known to be a player on the London club’s wishlist.
Chelsea submitted three offers for the England international defender last year, and he has remained a transfer target ever since.
However, Conte is reportedly unconvinced by Stones’ form for Everton and he regards Leonardo Bonucci as a better option.
Juventus defender Bonucci is apparently available for a fee of around £25 million, which would be half the price of what Everton are demanding for Stones.
Conte reportedly also considers Inter Milan's Andrea Ranocchia as a good option for the Blues, as his contract at the San Siro expires at the end of the season meaning he could be available on a free transfer.