Sky Sports reports that Liverpool boss Brendan Rodgers is keen to bring in Sturridge as a replacement for Andy Carroll.
Carroll left Liverpool for West Ham on Thursday.
Sturridge is reportedly interested in a move to Liverpool in order to get regular first-team football.
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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.