The former Liverpool defender thinks that Suarez should be playing at the very highest level, and therefore is also too good for Arsenal.
"Luis Suarez is too good for Liverpool," Carragher wrote in his Daily Mail column. "He is one of the top players in the world, whereas Liverpool were only the seventh-best team in England last season.
"His talents are greater than the stage on which he plays. Not only does he deserve to be playing in the Champions League, he should be winning it.
"Luis Suarez is also too good for Arsenal. In recent years, they haven't challenged for trophies, they haven't made an impact in the Champions League."