The Toffees have bolstered their midfield this summer, after spending a combined £60M to bring in Hayden Hackney, Tyrique George, Merlin Rohl and Christian Norgaard.
Brennan Johnson has also arrived from Crystal Palace - as part of a player swap deal with Dwight McNeil heading to Selhurst Park - but Moyes is still without a specialist option to replace departed former club captain Seamus Coleman.
Rohl has started at right-back in Everton's first two Premier League games of the season, amid reports Jake O'Brien has indicated he wants to play centrally moving forward.
O'Brien is on course to stay on Merseyside, despite exit rumours over the Republic of Ireland international, with Moyes closing in on a deal for Fulham's Kenny Tete.
Everton famously missed out on the Dutch star last summer, as he signed a contract extension at Craven Cottage, but as Alvaro Arbeloa looks to land Rayo Vallecano defender Andrei Ratiu - he could final make the move north.