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According to the report the 46-year-old former Serbia and Montenegro national team player suffered a knee injury and was taken to a local hospital, but it was not clear whether he was struck by a bullet or hurt himself falling.
Police are investigating the attack. They say unknown assailants shot from a car at Kovacevic as he was getting out of his car.
Kovacevic made 59 appearances for Serbia from 1994 to 2004. He played nine seasons for Real Sociedad over two stints and also had spells at Red Star Belgrade, Juventus, Lazio, and Sheffield Wednesday before ending his career with Olympiakos from 2007-09.