Mee, 22, made his loan from City permanent last week in a £900,000 deal.
But the City fan is planning to be back on their radar by winning promotion with the Clarets in May.
He said: "I'd like to get back up to the Premier League and play against City for Burnley - that would be the best thing. I had a great time there but this is a new chapter.
"I loved being there, but I have no problem moving, I just want to do my best here. I played once for City and would have liked more but that's the way it goes."