The reigning Premier League champions broke the British transfer record twice to sign Florian Wirtz and then Alexander Isak in the summer.
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Despite that, Carragher believes his former side need to spend even more cash in January to push towards the top of the Premier League.
Writing in his column for The Telegraph, Carragher put, "Pep Guardiola reacted to his club’s troubles by spending a combined £180m on Abdukodir Khusanov, Vitor Reis, Omar Marmoush, and Nico Gonzalez.
“City improved, preserved their Champions League status and are back fighting for every honour a year on."
Liverpool have been linked with January moves for Crystal Palace Marc Guehi and Bournemouth’s Antoine Semenyo.