The BFU said in a statement the Sofia-based club have 14 days to pay da Costa or face a three-point deduction in the domestic league under FIFA regulations.
CSKA signed da Costa from Romanian club FC Timisoara in September 2008 but only four months later the 25-year-old made a rare move to bitter city rivals Levski Sofia.
The BFU did not reveal the amount the 31-times Bulgarian champions owed the player, while CSKA are disputing the fine and are likely to appeal within the next seven days.
Da Costa has since left Levski Sofia. ($1=1.391 Leva)
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