The Liverpool born defender is widely expected to leave St Andrew's this summer as the club count the cost of relegation from the top flight.
A number of Premier League sides have been linked with the 24-year-old, including Arsenal, Liverpool, Stoke City and Chelsea.
Stoke are the only side to make a firm bid for the former Coventry defender, but their attempt to lure Dann to the Britannia Stadium failed last month and they are yet to come back with another offer.
Dann has made no secret of his desire to return to the Premier League at some point in his career but insists he is focused on the Blues for now.
"Obviously players have gone and that's just the way things have happened with the situation how it is now," Dann told the Birmingham Mail.
"From a personal point of view, I am still a Birmingham City player until I get told otherwise.
"I am an ambitious person and I want to play at the top level. Everyone who knows me knows that, and I am no different to any player.
"But at the moment all I am concentrating on is the football and doing well for Birmingham."