Everton are thought to value Jagielka (right), who they signed for £4m from Sheffield United in 2007, in the £18m plus bracket, but manager David Moyes remains likely to strongly resist any sale of a player he has earmarked as a future skipper.
Carsley told the Liverpool Echo: "I just think Jags is the perfect fit for Everton and vice versa. He is a player that David Moyes has worked hard with and given him a real chance to make the most of himself, which he's taken with both hands.
"I can't see why he cannot fulfil all his ambitions at Everton. There is no reason why they can't have a fantastic season and qualify for Europe again.
"Jags is already an England regular and that has come off the back of great displays for his current club so I just don't see why he would need to leave."