The 18-year-old, who is clocking Championship football at Bristol Rovers, has been attracting interest from a number of Premier League clubs.
Bids could come in for Scott in the summer, with Everton and West Ham keen, while Southampton have also been credited with interest amid scouts watching the midfielder in action.
Fleming knows that an offer might come in which Bristol City cannot refuse, but he insists that the club are not thinking about losing Scott, despite all the transfer talk.
“It’s something we don’t have to think about, at the moment he is our player”, Fleming was quoted as saying by Bristol World.
“The reality of football is if someone comes in and says I’ll give you £100m, we’d go alright then we might have to take that.
“But also if someone comes in and offers £400k you’d respond, are you winding me up?
“Nothing is going to happen here.
“We’re not thinking about him going, we haven’t even had it in the back of our mind.
“We don’t sit there shaking and thinking the phone is going to ring and someone is going to come and take him.
“We really believe that they are going to be here and the way that the club is forming, the plan and the pathway, young players are involved in that.”
Scott started at the weekend in Bristol City’s 2-0 loss at Nottingham Forest and clocked the full 90 minutes in the game.
The 18-year-old midfielder is locked down on a contract at the Robins until the summer of 2025.