And with many considering Liverpool’s triumph in the Champions League last season as an impetus to win the Premier League trophy, Carragher has insisted Manchester City are the side to beat by the Reds.
"I think it's a bit early yet. I think we've got to probably wait until Christmas," he said on Wednesday.
"I do feel around about Christmas time Liverpool and City will have a substantial gap and it looks like there's a little bit of a gap at this moment.
"But I still think City are favourites and are the best team in the Premier League at this moment because they won the Premier League and they proved that last season.
"So I think it's still on Liverpool to overtake City but they're more than capable."
After four games thus far, Manchester City are two points adrift table-toppers Liverpool who are yet to suffer first defeat.
Liverpool, who nearly ended their Premier League title drought for the first time in 29-years were pipped to the title by Manchester City by a point last season.
In a stellar spell at Anfield, Carragher was a member when Liverpool won the Champions League trophy in 2005, having defeated AC Milan 3-2 on penalties.
Resuming from the international break, Liverpool will host Newcastle for match-day five as City travel to Norwich City.
