Liverpool have enjoyed an encouraging start under Arne Slot and are top of the table after eight games as they sit one point ahead of their closest challengers Manchester City.
Slot's side face a big challenge on Sunday as they travel to face Arsenal, who are currently in third place.
Carragher believes that his former club are capable of winning the league this season but added that some action needs to be taken.
Liverpool are aiming to prevent City from winning the title for the fifth season in succession.
Carragher stated that Liverpool need to strengthen their squad in January in order to win the league.
According to Carragher, Liverpool need to bring in a top quality attacking midfielder, which would help to transform their team.
Carragher stated that Dominik Szoboszlai has left him 'wanting more' since his move from RB Leipzig in 2023.
Carragher wrote in The Telegraph: 'Liverpool need to grasp the nettle and make a couple of quality signings in January if they are to win the title.
'When comparing the full-strength Liverpool, Arsenal and Manchester City starting XIs, the title rivals have more quality in a particular area. Liverpool are short of a Martin Odegaard, Phil Foden or Kevin De Bruyne-style attacking midfielder – that X Factor in the middle of the park who elevates a side to the next level.
'Dominik Szoboszlai has performed well off the ball and he brings energy to the team – doing the ‘dirty work’ as he puts it – but for all the possession he gets in good areas, he needs to be more productive in terms of his assists and goals. We are yet to see if that is part of his game.
Carragher wants Liverpool to sign a midfielder and says Dominik Szoboszlai has left him 'wanting more'
'For the £60 million he cost, he too often leaves me wanting more. It does not need to all be ‘dirty’ work when you have the time and space on the edge of the penalty area to find a team-mate or unleash a shot.'
Furthermore, Carragher claimed that Liverpool need to recruit a new defender, who would ideally be able to perform effectively at centre-back or left-back.
Carragher continued: 'Liverpool also need another defender. I have been saying for a few years that the club needs a multi-purpose defender on the left – someone who can cover for Andrew Robertson or play centre-half without weakening the back line. Manchester City have those utility defenders in Nathan Ake and Josko Gvardiol. Arsenal’s Riccardo Calafiori comes into the same category.'
Liverpool had a quiet summer transfer window, with their only acquisition seeing Federico Chiesa arrive from Juventus.
If Liverpool were to bolster their squad in January then it could boost their chances of winning the title.