The Merseyside outfit have won their opening six games in the Premier League season to lay down an early marker.
Liverpool FC were 3-0 winners against Southampton at Anfield on Saturday a matter of days after the Reds eased to a 3-2 victory over Paris Saint-Germain in the Champions League.
The Reds are sitting at the top of the Premier League table and two points ahead of Chelsea FC and defending champions Manchester City.
Jurgen Klopp’s side have won their last three games against the Citizens in all competitions after scoring nine goals and conceding four times.
Former Liverpool FC defender Carragher believes the Reds’ record against the Premier League title holders could be significant.
“I think head-to-head between the top six will decide a lot,” Carragher told Sky Sports.
“Liverpool haven’t proven anything yet but they’re the one team in the league who seem to have given Man City a problem and can get under their skin.”
Liverpool FC finished in fourth spot in the Premier League table last term to ensure their continued participation in the Champions League.
The Reds finished in second place in the English top flight on three occasions under Gerard Houllier, Rafael Benitez and Brendan Rodgers in 2002, 2009 and 2014.
Klopp has led Liverpool FC to three cup finals but the Reds have lost to Manchester City, Sevilla and Real Madrid.
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