The Saudis are targeting the Croatia international on recommendation of captain Cristiano Ronaldo.
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Ronaldo played with Kovacic at Real Madrid and is a big fan of the City midfielder.
Al Nassr made a late bid to sign the 30-year-old before the Saudi transfer window closed on Monday.
However, they failed to offload Sadio Mané, 32, to make room for a foreign player.
Instead, Al Nassr will make another attempt with Kovacic when the transfer window opens in January, says CBS.
