The 19-year-old, who has been a key part of the club's first team this season, is regarded as one of the brightest prospects in the Championship.
His performances have reportedly attracted the interest of a number of Premier League clubs, but Clark has denied that they will sell the youngster.
Clark told the Birmingham Mail: "It would be a crazy decision to cash in on him. It would have to take big money, a fantastic offer, for us to part with him.
"Can we keep him? Yes, of course. Why not? He's a superb player. He's a local lad and he's enjoying his football."
Redmond has just one year remaining on his current deal.