Longtime observers trot out the hallowed names in the club's history and warn that greatness is partly defined by longevity. Others marvel at Suarez's breathtaking performances, week in, week out, and are beginning to wonder whether there has ever been a better player to wear the famous red shirt.
In the Kop's honors system, Kenny Dalglish is usually anointed in a category of his own. Most judges agree who should be crowned king and everyone else is playing for second place.
Does Suarez deserve to be mentioned in the same breath as the likes of Dalglish, John Barnes, Graeme Souness, Kevin Keegan, Billy Liddell, and modern-day greats Steven Gerrard and Jamie Carragher?
Absolutely. His displays are making an unarguable case for his entry into the very top tier of Liverpool players.
The high-water mark was the four-goal masterclass last week against Norwich City, one of the greatest individual performances in Premier League history. Yet the measure of Suarez's excellence is the consistency with which he is complementing prolific scoring with moments of jaw-dropping skill.
The dubious goals panel may rob Suarez of a third goal-of-the-season contender in four days, as his second against West Ham on Saturday took a heavy deflection off Joey O'Brien, but it does not take the gloss off the quality.
At a club whose history glitters with outstanding forwards — from Roger Hunt, Ian St. John, John Toshack, Kevin Keegan, Dalglish, John Aldridge and Ian Rush through to Premier League icons Robbie Fowler, Michael Owen and Fernando Torres — Suarez faces mighty competition for a place in the all-time rankings. Yet it is questionable whether any of the Uruguayan's gilded predecessors provided as big a threat to opponents as he is doing at the moment.
Like Dalglish, Suarez's excellence cannot be defined merely by numbers. His enterprise, touch and inventiveness demand that he is the first name on the team sheet whether he is finding the back of the net or not.
Nonetheless, the statistics are persuasive. In the 11 matches since his return from a 10-match suspension, Suarez has scored an astonishing 14 goals, all in the Premier League. In 107 games for Liverpool, he has scored 65 goals total. These are almost identical numbers to Aldridge (63 in 104), a penalty box predator who was being fed by Barnes and Peter Beardsley in arguably the most fluent Liverpool side of them all.
Suarez has become as prolific as any Liverpool forward in history, not bad for a player positionally categorized by Brendan Rodgers as a "nine and a half" and who was criticized for the sloppiness of his finishing during his earlier days at the club.
Technically outstanding, instinctive, two-footed, competitive and with an edge to his game, Suarez has all-around skills that have elevated him to the tier in world soccer directly below Lionel Messi and Cristiano Ronaldo. Like those two, his virtuosity matches his hunger and durability.
Even taking into account Suarez's temperament flaws, many indiscretions and the way he tried to engineer his exit to Real Madrid and then Arsenal last summer, the Uruguayan must command elite status in the Liverpool pantheon.
Yet exactly where depends on how long he continues to mesmerize in a red jersey. Liverpool will be confident of fending off interest from Real Madrid for its prize asset in January. Next summer promises to be a more testing proposition, with or without the carrot of Champions League soccer in 2014-15.
Should Suarez remain at the club, he could go down as the best Liverpool player there has ever been. There are few higher compliments.