Everton are on the hunt for a new manager following the departure of Roberto Martinez.
Everton failed to make it into Europe this season, meaning that they face a fight to keep hold of some of their prized assets.
The Toffees are expected to have to fend off offers for the likes of John Stones, Ross Barkley and Romelu Lukaku in the summer transfer window.
And Carragher claims that every potential new manager who is considered for the job at Goodison Park will be concerned.
“I think they have some great young players,” Carragher said. “I think the worry would be for a new manager coming in, is whether Stones, Barkley and Lukaku will stay. Some of those players, on the back of two disappointing seasons, are their heads going to be turned?”
Everton are looking for a new manager following the sacking of Roberto Martinez last week.
Martinez left Everton in 12th place in the Premier League, and although a final day win over Norwich City did move them up one place - their season has to be viewed as a disappointing one.
Everton have now been linked with a range of managers, as they look to find the right boss to take them forward.
The likes of Ronald Koeman and Frank De Boer are amongst the favourites to take over at Goodison Park.