Jagielka, 28, joined Everton from Sheffield United in 2007 and has gone on to establish himself as a key figure in the Merseysiders` defence.
His outstanding displays have seen Moyes' side climb to seventh in the Barclays Premier League table after a run of just one defeat in 10 games, and Moyes can not speak highly enough of the England international.
He told the Liverpool Echo: "What he has about him is as good as anyone in the country, it really is. He's a great recovery defender.
"There are bits of his game that will improve, but who could you not say that about? He is very valuable to us and that's why we have got him here on a long-term contract.
"I've said many times I see him as a future captain at Everton, and the way he's playing just now he's doing that."
Source: PA
Source: PA