In their yearly financial results, the Reds made an annual pre-tax profit of £125m - up from £40m - as turnover increased in the 12 months to May 2018 by £90m to £455m, also a record.
Liverpool were boosted financially by a run to the Champions League final last season, which earned an estimated £72m.
They were also helped by midfielder Philippe Coutinho's £142m transfer to Barcelona in January 2018.
Leicester City had held the record for net (post-tax) profit of £80m in 2016-17 (£92m pre-tax) after reaching the quarter-finals of the Champions League in 2017.
Having topped the Premier League table for much of the season, Liverpool are vying with defending champions Manchester City for a first English top-flight title for 29 years, and that success has been mirrored off the pitch too.
Media revenue has increased by £66m to £220m, commercial revenue by £17m to £154m and match revenue by £7m to £81m.
In revenue terms, Liverpool will leapfrog Arsenal into third place in the Premier League, behind Manchester United and Manchester City.
In total, £137m came into the club from player transfers. Liverpool say all of that has been reinvested back into the squad, taking outgoings on new players to more than £190m.
Andy Hughes, the club's chief operating officer, said: "What we have seen is a stable and sustained improvement in the club's financial position over recent years.
"This growth and increase in revenue has enabled us to significantly reinvest both in the playing squad and the football operational infrastructure.
"Financial results do fluctuate depending on player trading costs and timing of payments, but what's clear in these latest results is the further strengthening of our underlying financial footing and profits being reinvested in the squad and infrastructure."
The club also say their social media platforms had a 14% growth rate, taking the total to over 60 million followers across digital channels, and that in May 2018 they had the highest viewing figures ever for a Premier League club, and third of any sports club globally.
In January, Liverpool climbed two places to seventh in the latest edition of the Deloitte Football Money League.