Everton and England defender John Stones should reject a move to Chelsea in favour of remaining at Goodison Park and winning regular Premier League appearances.
The Daily Mail has reported that the Blues' third bid for Stones, understood to be of £30m ($47m), will be rejected by Roberto Martinez's team as they desperately attempt to keep hold of their star centre-back.
And Carragher, formerly of Liverpool and England, says the 21-year-old should remain at Everton for at least the next three years and rebuff a move to Chelsea for the time being. "It is very difficult for a young centre-back to be playing for a team right at the very pinnacle of the league," he told Sky Sports.
"The best place for him in the next two or three years is beside Roberto Martinez, at Goodison Park, playing and getting 30, 40, up to 50 games a season, getting experience under his belt. And then, no disrespect to Everton, maybe in two or three years he will be physically ready, mature as a player, and ready to move on. He's not ready now. The best place for that lad is to keep playing."
Martinez has been typically cautious about Chelsea's interest in Stones and has criticised John Terry for comments made in the media that appeared to identify the player as his replacement at Stamford Bridge.
Chelsea have begun the season with just five recognised senior defenders in their squad and Stones would assist in bolstering their resources as they attempt to retain their league title. But Martinez would prefer to see the transfer window closed at the start of the term, and says it is "unfair" that his team have to cope with rumours having already begun their campaign.
"The window, when it is open and we have to prepare for official games, is very, very unfair. I don't think it is right," the Spanish boss said. "I think we should have a period where we assemble our squad, and then once the first league game starts everyone is focused.
"I think we forget that footballers have a human side and it can really affect. Players like Stones and [Ross] Barkley have an incredible future and will attract interest from the outside. As a football club, these players are going to be a part of our success in the future, so we take [interest] as a positive compliment."