The 19-year-old has made the breakthrough into the Blues first team this season and the midfielder - who can also play at full-back - has played more than a dozen games for Clark's side.
Premier League neighbours West Bromwich Albion have been linked, but Clark is confident that despite Birmingham's relatively poor financial situation they will not sell Reilly as they have an option on his contract.
"It is no problem for us as he is one of the players who we actually have a contract option on," Clark said.
"Callum is living his dream at the moment as he is playing for his club.
"I am quite confident to say no matter which club came in for him if it is left down to him he would want to stay at Birmingham City."