Conte has been heavily linked to the post, which will be vacated by interim manager Guus Hiddink at the end of the season, with some reports suggesting a deal is already in place for the former Juventus coach.
And Vialli -??who led the London club between 1998 and 2000 - has likened Conte to another former Chelsea manager.
"In Italy they call him the Italian [Jose] 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."
Chelsea only have the FA Cup to play for after being eliminated from the Champions League by French champions Paris-Saint Germain in the round of 16 on Wednesday.
While a return to the continent's premier club competition next season is unlikely??with Chelsea 10 points adrift of the top four.