The 29-year-old, who scored a hat-trick against Tottenham last season, was a top target for the Clarets.
However, a Dinamo statement read: "In recent days, great interest of the public and fans has caused the possible transfer of player Mislav Oršić to the English club Burnley.
"Following this topic, GNK Dinamo informs the public that the decision has been made that Mislav Oršić will remain a Dinamo player and we are looking forward to participating in the continuation of the season together with his teammates and contributing to achieving the goal of winning a new Croatian title."
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