The Magpies failed in the battle with Juventus to land Elia just six months ago.
Newcastle boss Alan Pardew failed to persuade Elia to join the club when the winger left Hamburg.
Elia has failed to make the expected impact at Juventus and could leave the club, according to the Daily Mail.
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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.