The Daily Mail reports that Rodgers is keen to bring in Moses on a season-long loan.
Moses has been told he can leave Chelsea on loan in order to get regular first-team football.
Chelsea are reportedly asking for a £2million loan fee for the 22-year-old winger.
Moses has yet to make an appearance for Chelsea following the return of Jose Mourinho as manager.
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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.