The Belgian goalkeeper is set to depart the Stadium of Light this summer and according to the BBC Liverpool are the likeliest team to capture him.
Mignolet could be a replacement for Pepe Reina, who has been linked with a move away.
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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.