Leeds, who faced the Spireites in a pre-season friendly at the Proact on Saturday, made an undisclosed six-figure offer for Cooper which failed to meet the club's asking price.
Turner said: "We have turned down an initial bid which was below our valuation of Liam and we now await a response from Leeds.
"I'm not surprised that there has been interest in Liam because he is a quality player. Paul Cook has assembled a squad of players who are capable of playing in League 1 and above and it would be a surprise if none of them attracted interest from other clubs."
Cooper joined the Spireites on loan from Hull City in November 2012 and was signed on a permanent basis in January 2013.
He was a key member of last season's title-winning squad, forging a strong central defensive partnership with skipper Ian Evatt.