Carragher made the comments on Sky Sports after the tepid 1-1 draw at Old Trafford between Manchester United and the North Londoners on Monday.
The game came to life after Scottish midfielder Scott McTominay gave the hosts the lead with his first goal at Old Trafford right before halftime.
Arsenal drew level less than 15 minutes into the second half after their 18-year-old sensation, Bukayo Saka, threaded a nice pass to set free Pierre-Emerick Aubameyang, who clipped the ball past David De Gea.
The former Borussia Dortmund striker’s goal was initially ruled out for offside before VAR came to the rescue.
Carragher believes though it is early days yet, Chelsea will finish ahead of both teams.
He said: “The one team looking at that Manchester United vs Arsenal game who will be encouraged is Chelsea.
“At the start of the season, I thought Chelsea might struggle to get into the top-four.
“It will be a fight but even these early stages Chelsea have more quality than that we have seen from these two teams.”
This is Manchester United’s worst league start in 30 years and they have not scored more than a goal after their opening fixture at Old Trafford- a 4-0 win over Chelsea- despite facing teams like Crystal Palace, Astana and Rochdale.
Arsenal on the other hand have not kept a clean sheet in six consecutive league games.
