The Daily Mail reports that Moyes is keen to bring the Belgian forward to Goodison Park in January in a loan deal.
The 18-year-old joined Chelsea in a £18million deal from Anderlecht in the summer, but has failed to become a regular at Stamford Bridge.
Chelsea could decide to keep Lukaku at the club in January, should Nicolas Anelka or Didier Drogba leave.
Drogba has been linked with moves to Los Angeles Galaxy and Russian side Anzhi, while Anelka has been strongly linked with a switch to Chinese Super League side Shanghai Shenhua.
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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.