The Dutch centre-back has been a revelation since joining the club in January 2018, playing a major role in transforming Liverpool from top-four hopeful to Champions League winner and Premier League leader.
Before the coronavirus pandemic caused the indefinite suspension of top-level football, Liverpool were 25 points clear at the top of the English top-tier, potentially two wins from their first title in the Premier League era.
Van Dijk is widely considered a major reason for their successes, narrowly missing out on last year's Ballon d'Or to Lionel Messi.
The Netherlands international, 28, feels a connection with the club and is hopeful he will be seen as one of Liverpool's greatest players when he hangs up his boots.
When asked how he wants to be remembered when his career ends, he told Sport: "As a Liverpool legend. I want to achieve incredible things here.
"We have a fantastic team, we don't lack anything, we have all the tools necessary to on winning: a coach that we identify with, a versatile squad, a style of play that breeds victories, a stadium and supporters that play their part.
"Yes, I would like to be one of those players that return to Anfield after retiring. I see club legends at games and I feel part of a really big family."
Although a first league title in 30 years appears certain when the COVID-19 hiatus ends, Liverpool will not be retaining their European crown as they were eliminated by Atletico Madrid in the club's final game before the suspension.