The Uruguayan has since apologised for his actions and was fined two weeks' wages by the club, but there have been several calls for the Reds to sell their 30-goal striker in the summer.
However, Carragher feels that it will not be the case and thinks that there is a way back for the former Ajax forward.
"Now I am not for one moment trying to sugar-coat the incident in which Luis bit Branislav Ivanovic. It was wrong on all levels," he wrote in his column in the Daily Mail.
"Luis knows he has done something seriously wrong, letting himself down. But, rather than hounding him out of the country, shouldn't we be helping him? We have a top psychologist in Steve Peters who comes to the club once a week and he could have as big a role as our manager, Brendan Rodgers, for Luis.
"People may say this is a Liverpool-biased opinion but I don't want to see another world-class player leave the Barclays Premier League, like Xabi Alonso, Cristiano Ronaldo and Cesc Fabregas have. We are talking about one of the top five players in world football here."
Suarez accepted a charge of violent conduct from the Football Association yesterday.