Ian Rush
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As is the case with John Barnes, if this countdown included the full Liverpool career of Ian Rush then he would be noticeably higher on the list.
Liverpool's all-time leading scorer is one of the great strikers in British football history, but his most prolific spell came before the advent of the Premier League when Liverpool swept all before them in the 1980s.
Having returned to Anfield in 1988 following a brief and unsuccessful spell at Juventus, Rush spent eight more years at Liverpool to take his overall tally for the club up to 346 goals.
Only four of those years were spent in the Premier League, though, during which time Rush scored 45 goals in 130 league outings and 67 in 170 games across all competitions.
Of his 14 major honours at Liverpool, only the 1995 League Cup came in the Premier League era as Liverpool's grip on English football began to loosen, and Rush eventually ended his long association with the club in 1996.
The Wales international was still the club's top scorer in their first two Premier League seasons, though, and acted as a mentor for the up-and-coming Robbie Fowler, who took over the mantle as Liverpool's main front man towards the end of Rush's Anfield career.