Zigic made the £6million move from Valencia to Blues during the summer transfer window.
He has so far struggled to command a regular first-team spot although he did net his first Barclays Premier League goal last weekend against Arsenal in a rare start.
But the Serbia international has laughed off claims that he will be ready to leave City after only a few months and he said:
"I was aware of the speculation about Sporting Lisbon and I found it quite amusing."
He continued: "But really I am a Birmingham player. I enjoy being here. I am certainly going to try my best for the club and something I want to do is progress my career here.
"You always get some speculation from other clubs and what have you.
"But I am a Birmingham player, I signed a contract in the summer, I enjoy playing with the boys, we are a good squad and I'm more than happy being here."
Zigic has found it difficult adjusting to the different style of the Premier League compared to the technical football in Spain.
He said: "Because of my height, the ball does come up to me to knock on.
"But I am a bit more of a technical player than people give me credit for. I do like the ball into my feet."
Zigic is set to retain his place for Saturday's home clash with Blackpool especially as last season's top scorer, Cameron Jerome, is still doubtful with an ankle problem.