The Uruguay striker publicly declared his desire to leave Anfield on Tuesday, although manager Brendan Rodgers has warned him that he must accept the club’s policy not to sell him to Arsenal.
However, Carragher believes Suarez’s ability warrants a move to one of Europe’s top clubs, although he stipulated that a move to the Gunners would not make sense for the 26-year-old.
"Luis Suarez is too good for Liverpool," the former England and Liverpool defender wrote in his column for the Daily Mail. "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 play 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 have not made an impact in the Champions League and they are no closer to winning the Premier League.
"If Barcelona, Real Madrid or Bayern Munich wanted him, I would wish Luis all the luck in the world and staunchly defend him.
"That is his level; teams who have a great chance of winning the Champions League. That’s why I'm so puzzled by his determination to leave for the Emirates."
Carragher recently took part in a Liverpool training session in preparation for Steven Gerrard's testimonial, and he says he was alarmed at the effort put in by the Uruguayan, who has since been made to train alone.
"He didn’t want the ball and had no interest in getting involved. He stood on the periphery, with shoulders slumped," he continued.
"It didn’t surprise me that Brendan Rodgers has made him train on his own. I never thought Luis would down tools in the way Fernando Torres did when he wanted to leave Liverpool - his attitude over the final 18 months became progressively worse - but now Suarez has given me reason to think again.
"To see it come to this is very dispiriting."