The Daily Mail says the Blues are lining up a new contract for Digne after tying down Richarlison.
The Toffees confirmed Richarlison's extension which will run until 2024 on Tuesday.
The Brazilian forward only joined Everton in 2018 on a five-year deal and has already been rewarded with an improved contract.
The Goodison Park club now want to do the same with left-back Digne.
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