Terry is assistant to Dean Smith at Villa, and is being linked with the manager's job at Championship club Bristol.
But Hutton thinks Terry may not be interested in the role, especially if Villa are still in the Premier League next term.
"I'm not so sure – until he comes out and physically says it, I wouldn't really believe it," the former Tottenham and Scotland player told Football Insider.
"He's going to make a fantastic manager, I've obviously worked with him up close at Villa and seen how meticulous he is in certain aspects of the game, I know what kind of guy he is.
"Whether that's the first one he would fancy, they are a decent side, mid-table in the Championship, I don't know if that's the first one he would want to take but he will want to step out on his own two feet at some point in the foreseeable future.
"Whether that's the first one he'd choose, I'm not sure."