After retiring last summer, Terry became assistant coach at Villa, who earned promotion to the top flight this spring.
According to Di Matteo, who played at Chelsea between 1996 and 2002 before leading the club to the Champions League title as head coach in 2012, the former England captain will one day fill the managerial position at Stamford Bridge.
“He, too, will be there as a manager in the future,” the Italian told The Athletic.
“As a player, he was writing down some of the sessions and he’s now gained so much experience from the managers he’s worked under.”
Di Matteo also backed current Chelsea manager Frank Lampard – another former Blues player and teammate of Terry – to succeed at Stamford Bridge despite mixed fortunes in his first few games in charge.
“Frank will become a great manager,” Di Matteo said.
“He is a very balanced guy – sensible, smart and incredibly hard-working.
“I think it’s the right appointment for Chelsea, because it brings everybody together.”
Meanwhile, Villa have lost three of their four league games since the start of the season.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies