The Toffees are set to pay £4.2 million to sign the ex-Arsenal defender, per Sky Sports.
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The former England international is in his final year with the French outfit.
Everton tried to sign Maitland-Niles previously, and it looks the deal will finally be done on deadline day.
A versatile operator, Maitland-Niles can play as both a full-back and a midfielder.
Maitland-Niles has made 85 appearances for Lyon across three seasons, and will be making a return to the Premier League to play under David Moyes this season.