The Spanish forward has been heavily linked with a move to Tottenham, with Arsenal and Liverpool also linked.
However Napoli, who are looking to replace Edinson Cavani, may turn to Soldado after struggling to do a deal for Gonzalo Higuain or Leandro Damiao.
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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.