Carragher's comments came in the wake of Arsenal's 2-0 win over Everton on Sunday, with the 'Sky Sports' pundit of the opinion that both the 'Gunners' and the 'Red Devils' will come up short.
"On the evidence of what we've seen I'd say Arsenal or Manchester United from what we've seen in these opening six games. The others look a little bit further up," he explained.
"Tottenham have had a little bit of a wobble, a good result for them yesterday but it will be really tight and it always is with the top six.
"I think the top six are so far ahead now that if just one or two of those teams on any given weekend drop points it feels like a really big thing for the rest of the other teams, because a lot of the other dropped points come from each other.
"So far Liverpool winning, City winning, for Tottenham and Arsenal, for Chelsea and United to drop points against two of the lesser sides it's a really big thing.
"City showed last year - and whoever is going to win the title this year - that the points total now to win the title - it was 80 or so when I was playing - but it's 90 plus now."
Liverpool currently lead the division with 18 points having won all six of their games so far, with Chelsea and Man City trailing them both by two points having drawn a single game.
Surprisinly, Watford sit in fourth, a point ahead of Tottneham and Arsenal, with United all the way down in seventh having won just three of their six games to date.