The 18-year-old midfielder is reportedly on the radar of Manchester United and Tottenham following an impressive breakthrough season.
But Mowbray, who this week signed a new two-year contract with the Sky Blues, has made hanging on to Maddison a priority.
“The phone has rung once or twice but the message has been loud and clear. We want to keep him,” said Mowbray at a press conference on Tuesday morning.
“He’s just starting on the ladder, let’s get him in his boots and on the pitch for us. What’s the point of going to a big club and training all the time?
“He needs to get his head down and work hard and bide his time and help us to be successful.”
Mowbray has begun reshaping his squad ahead of next season by releasing Frank Nouble, Adam Barton, Andy Webster, Shaun Miller, Simeon Jackson, Al Bangura, Danny Pugh and Blair Turgott.
He added: “Two years is enough time to hopefully build a squad to be in the image I want. That’s the exciting part, to build a team from scratch.”