However, the Liverpool legend has been impressed by Manchester United so far this pre-season.
Louis van Gaal's side beat Real Madrid on Saturday night to reach the International Champions Cup final against Liverpool, who Carragher also says have looked impressive, to record their fourth friendly win out of four.
First came a 7-0 triumph against LA Galaxy, then a 3-2 win over Roma. United followed it up with a penalty-shootout win over Inter Milan before beating Madrid 3-1 with a comfortable victory.
Such form has made an impression on the former Reds defender, who believes Man United already look a better side than last season.
And yet there is only one team Carragher thinks will lift the Premier League trophy this season. Not United, not Liverpool - and not defending champions Manchester City.
Chelsea my tip for the title.— Jamie Carragher (@Carra23) August 3, 2014
Yes watched the two games Man U and Lfc both look impressive in pre season.— Jamie Carragher (@Carra23) August 3, 2014
Man U certainly look better than last season but only pre season games although they struggled in pre season last season so may bode well.— Jamie Carragher (@Carra23) August 3, 2014
Chelsea have strengthened the squad that finished third in the league and reached the Champions League semi-finals last term considerably this summer, adding the likes of Cesc Fabregas, Diego Costa and Filipe Luis to Mourinho's squad.
Didier Drogba has also returned to Stamford Bridge and many have been impressed enough to make the Blues their Premier League favourites.
Carragher is one of them, although his former club Liverpool may have something to say about that come the business end of the season.
The same can, of course, be said of City and perhaps even Arsenal, while Van Gaal will hope his winning habit will continue at Old Trafford when the new campaign begins.
Do you agree with Carragher's comments about United and Chelsea?