Aston Villa and Southampton are among the clubs interested in signing the talented youngster, report Corriere dello Sport.
Coutinho has struggled for playing time for the Nerazzurri, having been on loan in Spain last season.
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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.