Suarez is expected to find out in the next 24 hours whether FIFA's disciplinary committee considers him guilty of biting Giorgio Chiellini during Uruguay's World Cup win over Italy.
A ban would likely follow any guilty verdict, and it is within FIFA's remit to extend any suspension to his club football.
That would be unfair on Liverpool, according to Sky Sports pundit Carragher, who was still on the Anfield playing staff when Suarez bit Chelsea's Branislav Ivanovic in April 2013 to earn a 10-game ban.
The Ivanovic offence followed a similar attack on an opponent during Suarez's time at Ajax, but Carragher told Sky Sports News: "I don't agree with a worldwide ban. The last time he was banned Liverpool lost him for 10 games, but I think he still played for Uruguay.
"This is an international tournament, a FIFA tournament, the biting incident is in a Uruguay shirt and it should be Uruguay and Luis Suarez who pay the consequences.
"I would expect he'll miss the rest of the World Cup. He had seven games for the Ajax incident, 10 for the Liverpool one so you may expect it'll go to a 12 or 15-game ban - in international football that could be more than 12 months. I don't think Liverpool should be affected."
Suarez was being heavily linked with Real Madrid and Barcelona even before the Chiellini incident, and Carragher believes Liverpool may now be less inclined to fight for their star man - as long as their asking price is met.
"It's all about money," he said. "Of course the club will not be happy with the scenes, and Luis won't be happy himself, but it all comes down to numbers.
"Liverpool are not going to let an £80-£100m player leave for a cut-price fee, but if someone did offer that type of money I think now they may think 'take the money'.
"I certainly don't think Liverpool should be looking to get rid of him on the cheap. If someone pays top dollar I think now may be the time, but if they don't then I don't think Liverpool will sell."
Woah! 'Failed to teach him.' We are talking about a 27 year old man! He is responsible for himself, and due to the huge amount of fans and all the cameras must be held accountable. He needs to be banned from football because of the risk he will do it again and for protection of the multi-billion dollar brand which is football. It's a shame for Liverpool FC as they didn't really do anything..... Though I don't feel that sorry for them after all the T-shirt b0ll0cks. And the continued blinkered support of the likes of @AmericanScouser. Just imagine Americanscouser... the possibilities should he have played all last season or all this season.... guess we'll never know. But support him all you like- he was part of the reason your still waiting for a league title.- wozza