The Sky Blues were linked a couple of weeks ago with the 25 year old striker who has played for Exeter, Stevenage, Leyton Orient, Northampton, Tottenham and Crewe.
Barnard is out of contract at the end of this season and his Chairman Ron Martin, told The Echo: "Of course the club doesn't want to sell Lee but clearly he will not sign a new contract and I am told he will walk at the end of the season.
"We're between a rock and a hard place. "However, for the moment no decision has been made and whatever decision the manager and board comes to, it will serve the best interests of the club."