Corriere dello Sport claim that an agreement is close to being finalised between the two parties.
Garcia has forged a reputation as a fine coach during his time in France, winning Ligue 1 with Lille in 2011.
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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.