Arsenal reportedly saw a £12 million bid for Jagielka, 29, turned down by Everton this summer, and speculation this week has suggested the Gunners could renew their interest in the England international.
But Moyes told the Liverpool Echo: "I have had two or three conversations with Jags and he is up-to-date with everything and anything that has happened.
"He has said to me that, unless it is something Everton want to do, he is not going to be the one who instigates or pushes anything. It will only be if Everton want to do it and I certainly don't want to do it."
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