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The defender, 36, joined Championship club Aston Villa on a one-year deal on Monday after leaving the Premier League champions at the end of June.
Quoted in several national newspapers, Terry said: "Do you dream too big? I don't think you can ever dream too big.
"I've always wanted to be the very best and if that's in management, then Chelsea's the one."
The former England captain, who made 717 appearances and won five league titles with Chelsea, added: "That would be incredible but I realise as well you can't go in somewhere like Chelsea as your first job."
Speaking at his unveiling after joining Villa, Terry said the difficulty he would have in facing Chelsea was one of the main reasons for him turning down offers from Premier League clubs.
Terry will not have a coaching role at Villa, but is eager to learn from manager Steve Bruce and director of football Steve Round, with whom Terry worked during his international career.
"They played a huge part (in him signing)," he told BBC Radio 5 live. "The dialogue I've had with them was key.
"I looked up to Steve Bruce as a player, and as a manager I'm looking to come in and learn from him.
"Steve Round was a very good coach with England and, although he's got a different role now, he's still got that football knowledge and knows how to deal with players professionally and personally.
"They've shown me a lot of respect, they want me at their football club and that meant a lot."
John Terry has said it would be "incredible" to manage his former club Chelsea once his playing career ends.