Reilly, 19, born in Cheshire but raised in Solihull, rose through City's academy system before making his first-team debut as a late substitute in an FA Cup tie last season, his sole appearance of the campaign.
His real breakthrough has come this year under manager Lee Clark, with Reilly handed his first start in mid-December and going on to enjoy a total of 16 appearances since.
The player's performances have attracted international recognition for the Republic of Ireland Under-21s and, according to reports, alerted the likes of West Brom to his services.
Despite being one of a host of players out of contract this summer, Blues hold a further 12-month option on Reilly's current deal, and the teenager is keen to remain at St Andrew's and continue his development.
"I would be delighted to stay at this club," he told the Birmingham Mail. "That's all speculation. I haven't heard anything about that, other clubs. I love it here. I'm just learning off 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."
And boss Clark anticipates no problems when it comes to tying Reilly down to a new contract at Birmingham.
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. He's playing for the club he supports and I think he's more than happy here."