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The England international joined the Reds from Chelsea in January 2013 and quickly established him as a key member of Brendan Rodgers’s squad.
Sturridge is now looking to cement his place in Liverpool history and become a club legend.
‘The fans have had songs for Kenny Dalglish and they still live on’, Sturridge told Liverpool’s official website. ‘The same with Robbie Fowler. Even at away games, sometimes you'll hear them singing songs about Ian Rush.
‘Luis [Suarez's] song was always sung last season, so hopefully I'll have a song one day as well - and not just a song, to go down as one of the best players is always great. It's something every player wants, whether or not they say it out loud.
‘Every player wants to be recognised as one of the best to have played for their club. It's going to be a difficult task because there are so many who have done it before [me] and there'll be so many who do it after’.
However, the ex-Denmark international claims that the Merseyside outfit need to start picking up wins quickly in order to achieve their objectives this campaign.
‘We’re only three points behind Arsenal in fourth and everything we wanted to achieve this season is still there to be had – reaching the knockout stages of the Champions League and finishing in the top four of the Premier League’, he wrote in The Liverpool Echo.
‘There’s plenty of time to put things right. But we need to get going before it reached desperation levels as then it becomes very difficult to play. We don’t have to be winning by three or four, we just need to start grinding out results’.