The Italian, who is currently in charge at League One side Swindon Town, played for seven years in the Premier League with Sheffield Wednesday, West Ham United and Charlton Athletic.
"The dream is, once I am well known here and settled in this environment I love, to be the manager of England," the 44-year-old told The Mirror.
"Maybe it will never happen, because they'll never give it to me.
"I dream to be the foreign hero who leads England to victory after so many decades."
Di Canio has recently been linked with the vacant manager's position at Championship club Bolton Wanderers.