That is according to Gazzetta dello Sport, who claim the Inter Milan supremo has phoned Mourinho to sound him out about a return and make him aware of his interest.
Mourinho is set to leave Real Madrid this summer after alienating figures there with his antics.
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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.