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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.