Suarez has not been shy in voicing his discontent with life in England in recent weeks, and has repeatedly spoken of his desire to one day play for Real Madrid.
Liverpool have so far remained steadfast in their public determination to keep their unsettled star, but Carragher believes forcing him to stay could do more harm than good.
“The thing about keeping unhappy players is an issue because we had that experience with Torres, and keeping him definitely wasn’t the right thing to do,” he told Sky Sports.
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“I do believe that Suarez is a slightly different character to Fernando Torres.
“There were times, I believe, Torres wasn’t giving his best on the pitch for Liverpool and that is why it was a mistake to keep him.
“I don’t think that will happen with Suarez, simply because of the player he is. But it is something you must be aware of.”
Suarez's desire to join Real Madrid appears to be reciprocated by the Spanish giants, and Carragher is unsurprised that the Uruguayan is attracting such illustrious suitors.
“Luis is one of the best players in the world and, when Real Madrid come calling, it will obviously turn a player’s head - he’s obviously had his head turned, but which player wouldn’t?" added Carragher.
“Liverpool would have known they were always going to be in this situation, with other clubs calling for Luis Suarez this summer.
“If you were honest, Luis Suarez is playing in a team that finished seventh in the Premier League, but he is one of the best players in the world.
“Liverpool just can’t roll over and accept Luis Suarez will leave, but if he goes, they must get top dollar for him.
“If he was to be sold, it would be up to the club to make sure that the money was spent in the right way, after maybe not doing that after Torres went.
“They have to be decisive. They either wait for a bid they think is acceptable or they decide to keep him because he is Liverpool’s best player and they want to build a team around him.
“Whichever way, they need to act. If you lose a player late, it’s very hard to replace him at that stage of the window.”