Former Goodison boss Moyes is the No 1 choice of Toffees chairman Bill Kenwright and remains favourite to succeed the Portuguese.
Majority owner Farhad Moshiri — after first going along with Kenwright's plan to bring back Moyes — is now being contacted by agent Kia Joorabchian.
He not only represents Hughes but also Toffees' Brazilian stars Bernard and Richarlison and is understood to be offering not only the Welshman but a host of possible transfer targets.
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