The veteran defender has played against both the Real Madrid and Barcelona stars during his career with the Reds, and feels that although they are the two finest players on the planet, they will never be considered friends off the field.
"They emit mutual loathing rather than mutual respect," Carragher said in his column in the Daily Mail.
"They are the best players in the world but they will never be best friends. You don't need to be a body language expert to appreciate there is no love lost between these two.
"Ronaldo was pictured with a face like thunder when Messi was presented with the Ballon D'Or [in January]. On the other hand, Messi has not once said in public how good Ronaldo is."
The two players played for their respective sides on Tuesday, as Madrid beat Barca