The American businessman recently stated that it would be "ludicrous" for the club to sell the Uruguayan, who has publicly stated that he wants to leave Anfield following interest from Arsenal.
"If you look at how strong John W Henry has been on Suarez, I think it is great for football that a chairman has come out and said a player is staying," Carragher told BBC Radio Five Live. "Hopefully that can be a message right across the country.
"Suarez signed a contract last season. He does not have to honour the whole contract but there are ways and means of going about it. It now looks like he is staying. Now, he has to show the form he has shown over the last few years."