The Scotland international's former manager Alex McLeish tried to take Burke to Nottingham Forest, while Leeds United also showed an interest in the 29-year-old.
Birmingham resisted offers for Burke and the former Rangers man proved his worth by scoring both goals in Saturday's 2-1 home win over Forest.
"I've always said I love it at Blues and I want to stay here," said Burke.
"If you start listening to speculation then maybe that can affect you."
Blues did sell Jack Butland to Stoke City last month, but the goalkeeper returned to St Andrew's on loan and Burke believes it will be positive for the club for the rest of the season.
Burke added: "This win is a massive boost for us and you can only take positives from that.
"Getting Jack back could be crucial for us between now and the end of the season, he's handled it all very well.
"I think it's the first time we've had back-to-back victories this season. We know we've been underachieving as a squad and we have to pick up on that and be more consistent."