Suarez has declared he wants to leave Anfield this summer.
"Luis has to be playing Champions League football," said Cavani. "When you have the most complete striker in the world not playing in the top competition in Europe, then you know something is not right. He deserves the Champions League and the Champions League deserves him.
"Real Madrid are a great team; Chelsea are a great team and Arsenal are a great team – but the most important thing is that they can offer him consistent Champions League football, which is not something Liverpool have been able to do.
"I can tell you his love for Liverpool is very real. If they were playing in the Champions League, he would not consider leaving. But he knows he is now at the stage of his career that he needs to be playing at the top level."