The Daily Mail report that the Gunners are keen to make an early move for the player before other sides join the chase for Jovetic.
£25 million may be needed to prise the Montenegrin forward from Fiorentina.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.