The 19-year-old has burst onto the scene at St Andrew's this season, with his performance level in the Championship drawing plenty of admiring glances from afar.
He is said to have attracted Premier League interest, with West Bromwich Albion among those believed to be monitoring his progress.
Reilly will see his current contract expire at the end of the season, fuelling the transfer flames, but Birmingham hold a one-year extension option and are expected to activate that clause.
The highly-rated midfielder would be delighted if they do, with it his intention to continue working on his game with the Blues before looking to take a step up.
Reilly told the Birmingham Mail: "I would be delighted to stay at this club.
"That's all speculation, I haven't heard anything about that, other clubs. I love it here, I'm just learning from the manager and playing my game the best I can.
"I'd love to play a full season, get a whole season under my belt, and then kick on from there."
Birmingham boss Lee Clark is confident Reilly will be at his disposal next season and is reading little into the speculation regarding his future.
He said: "I have no issues, no worries over Callum, and I'm not being complacent when I say that.
"It's great when other clubs notice our players or are interested in them, it means they're doing well.
"Callum has come in and made an impact for us this season. He's young and he's going to improve further.
"He's a massive part of our future and I can't see there being a problem sorting out a new contract."