Pep Guardiola's team remains undefeated this season and currently holds the second position in the Premier League standings. They are just one point behind league leaders Liverpool, having played eight games so far.
Last season's runners-up Arsenal suffered their first loss of the season in a 2-0 defeat at Bournemouth, which has left Mikel Arteta's side four points off the top.
The Gunners host Liverpool at the Emirates Stadium on Sunday, live on , but before that game City could go top with victory at home over winless Southampton on Saturday - and Carragher feels the champions remain favourites to claim a fifth straight Premier League title.
He told News: "I still think Manchester City, without a doubt, have an edge on Liverpool. And probably just Arsenal, maybe.
Trending"You change your mind every week, don't you on the back of results, but I still think City are the team to beat - and Liverpool and Arsenal, you can flip a coin."
Carragher, however, does feel the reigning champions are susceptible to counter-attacks this campaign following the season-ending injury to Rodri.
City have only kept one clean sheet in the league this season and conceded a counter-attack goal in their recent win over Wolves, while giving up multiple chances to Fulham on the transition.
"I think they do look a little bit more vulnerable to the counter-attack," Carragher said. "That's always the way to hurt Manchester City, because they have so much possession.
"The only way you can really score or hurt them is set-pieces and on the counter-attack.
"I think missing Rodri will hurt them. I think it'll hurt them more in the Champions League, when you're playing higher-class opposition when you get into the quarter-finals and semi-finals. That's when they may feel it a little bit more.
"I still think they can win the league without Rodri, even though he's one of the top players in the Premier League."
City sit a point behind Liverpool after the Reds beat Chelsea on Sunday 2-1 at Anfield to regain top spot following City's victory at Wolves.
Arne Slot became the first Liverpool boss to win 10 of his first 11 games, with the Reds' electric start coming despite only signing one first-team player for this season in the summer.
Carragher believes his former side will make a signing in January if they are in the running for the title.
He said: "They're very much pushing [to win the Premier League title], as they were last season. We shouldn't forget that.
"They haven't reinforced. It'll be really interesting to see if Liverpool do bring anyone in in January. They didn't bring too much in in the summer.
"And if they think they've got a realistic chance at the title and there's a player that they feel fits their criteria, their model, I think they'll pay the money to bring that player in."
City's closest challengers for the last two seasons, Arsenal, received their third red card of the season after William Saliba's sending-off in the Bournemouth defeat.
Carragher insists the Gunners' disciplinary issues must be resolved if they are to lift their first Premier League title in 21 years.
Asked whether Arsenal's disciplinary problems will ruin their chances of winning the league, he replied: "Yes, if it doesn't stop. It has to stop quickly.
"To get three red cards in the first eight games of the season is really poor. They may feel a little bit hard done by on certain issues, but when I look at all the situations, they're deserved red cards. I don't think they could really argue too much, and it's cost them.
"You think of the positions they found themselves in. They were beating Brighton at home when the red card comes, they were beating Manchester City away when the red card comes, and it was level at Bournemouth.
"So they've dropped points in all the games from the situation that they found themselves in, 11 v 11. It's a huge problem."
Carragher added on Monday Night Football: "This has got to stop. You're talking about a team in Manchester City that are already three points ahead [of Arsenal] - you can't afford to let someone like that get away from you.
"You look at Manchester City and Liverpool and they can still win games in that situation. So you have to ask yourself about Arsenal's set-up in those situations - is it right tactically how they're going about it?"
Watch Arsenal vs Liverpool live on Premier League from 4pm on Sunday; kick-off 4.30pm.