Patrice Evra claims Jurgen Klopp's Liverpool cannot be deemed a great team unless they win three consecutive Premier League titles.
The Reds comfortably beat Leicester City - who were the league leaders going into this weekend - 3-0 at Anfield to move level on points with Tottenham Hotspur at the top of the table.
The victory, courtesy of a Jonny Evans own goal and strikes from Diogo Jota and Roberto Firmino, also extended Liverpool's unbeaten home run to 64 games - surpassing the current club record set 40 years ago.
But former Manchester United defender Evra believes this current crop of Liverpool stars cannot be deemed the greatest ever unless they make a top-flight title triumph a regular occurrence at Anfield.
The Frenchman told Sky Sports: 'We need to calm down, it’s only 9 games. I will call them a great team when they win three league titles in a row.
'If they don’t win this year, I won’t call them an amazing team – it’s all about consistency and they win the league year after year – that’s when we call them the great Liverpool team.
'Many teams before that have done that and I will call them the best Liverpool team when they win three leagues in a row.'
Fellow Sky Sports pundit Freddie Ljungberg, who won two league titles at Arsenal in 2002 and 2004, also believes this current Liverpool side are not the best team they have produced.
The Swede claimed: 'It’s a great, great club and to say they’re the best team compared to other histories and team, I don’t think that’s fair. I agree with Patrice though.'
Liverpool lifted their first ever Premier League title back in July, ending a 30-year wait for a top-flight title in England.
It was the Merseyside club's 19th league title overall, with only fierce rivals Manchester United picking up more with 20. The Reds last won three league titles in a row back in the 1980s which they completed their triple crown between 1981 and 1984.
Evra was part of the Manchester United side that won titles 16 through to 20, including three in a row between 2006 and 2009, but concedes that Liverpool will be a title challenger for years to come.
The 39-year-old added: 'They (Liverpool) are sending a massive signal to their title rivals and now they’re even stronger.
'Liverpool will be a massive challenger and I won’t be surprised. Big club – that’s all I have to say.'