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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.