Blues boss Alex McLeish has offered the former Celtic star a trial spell with a view to joining the club.
However, the Guinea international defender has revealed that Burnley have offered him a permanent deal straight away.
"I have an offer of a trial with Birmingham. They have asked me to join them for pre-season when they return on July 8," said Balde.
"The club have already told me there will be a two-year contract on the table for me if I do well and impress during my trial period.
"Burnley have also made me an offer, but unconditionally.
"I will have to have a think about things before I decide my future.
"My career is changing in such a way that I must accept the situation.
"I am 33, I have not played much over the last 12 months and I am not in a position of strength.
"When a player is inactive, they lose the rhythm and habit of duels. This is my case and I must accept it."