The 20-year old has grown in stature this season and with a few injuries to regular Three Lions midfielders, could be a chance for a promotion according to Moyes.
"I think a senior call-up can come too early. You want it to be merited for the right reasons," said the Toffees boss.
"You want him to go into the team. If he played he wouldn't let anyone down because in international football he has some very good qualities.
"Jack has done well. He has improved over the recent weeks and I think because of that he is getting close (to the full England team).
"He is obviously going to be mentioned. He has played well in the games.
"Is he ready for the big full international stage? That is something we will all need to wait and see."