The Ghana international is in talks to sign on-loan for the Toffees, reports The Times.
Kudus has struggled for regular senior football at Ajax since arriving two years ago from FC Nordsjaelland for €9m.
Ajax coach Alfred Schreuder recently said: "He can play in the front as a striker, but also on the right and left.
"I did say to him: don't start thinking: oh dear, the trainer no longer sees me as a midfielder, it's not like that. But I am charmed by him in the front. He is a very interesting attacker for Ajax, because he plays very much from intuition. As a defender that is very difficult to play against. He is strong, fast and does things that no one expects."