The Reds appear in rude health, both on and off the pitch at the moment, with positive financial figures complementing a competitive, successful team, led by boss Jurgen Klopp.
A sixth European Cup was secured in June, less than a month after they were narrowly pipped by Manchester City to the Premier League by a point, despite a tally which would have guaranteed top spot in 25 of the last 27 seasons.
The league resumes this weekend after the international break with Klopp's side - in possession of the only 100 per cent record in England's top four divisions - eight points clear of City and set for another title challenge.
Moore says above everything else the dream is to be crowned champions of England again and end the club's 30-year wait for the title.
"I think that is what our fans want," he told the Press Association. "We were so close last year, 97 points, and in any other year we would have won it. But the club goes on and I think that (a league title), for many of our fans, would sit alongside our Champions League triumph as the barometer of success.
"As a club off the pitch we have a set of visions, missions and values and at the top of that sits supporting the team to win trophies.
"We feel good about the club in its entirety and we don't compare ourselves with any other football club."
Moore believes the evolution at Anfield has been a gradual process since they were taken over by the then New England Sports ventures group in 2010.
Now called Fenway Sports Group, headed by John W Henry, the club is completely geared up to be successful, unlike under previous regimes.
He added: "What Liverpool had to do was bring in a world-class manager, which we have, bring in a world-class squad, which we have, play exciting football, bring in players that are going to draw crowds no matter where they go - we've done that - build financial security at the club, we've done that."
Liverpool go to long-standing rivals Manchester United on Sunday aiming to make it nine straight wins from the start of the season and also equal City's record of 18 consecutive Premier League wins with Klopp's side not picking up anything other than a win since March's goalless draw in the Merseyside derby at Everton.