However, after a meeting with the manager, the 33-year-old full-back has been assured of his future by the Blues boss and is hoping for a new contract that would see him finish his career at St. Andrew's.
"My immediate reaction was 'is that me out of the door then?' But I went to see the manager and I heard everything I wanted to hear," Kenna told the Evening Mail.
"He told me that he wanted to strengthen down the right-back position and that's entirely his prerogative, I've no problem with competition.
"He said that if Danny Mills had signed, that wouldn't have been the end of me, and around Christmas time, if I'm still in the team, he'll come to me and sort out a new contract.
"I know that I would be probably very fortunate to get a two-year contract at any club, not just this one.
"But hopefully this won't drag out and we can get something sorted because I'd very much like to stay here and I still think I've got a lot to offer."
