Several members of Moyes’ team will not be back on Merseyside until later this month, due to World Cup duty, but the Toffees boss has a core of players to work with at Finch Farm in the coming weeks.
Among those in the ‘non-World Cup squad' is defender Jake O’Brien after he missed out qualification as the Republic of Ireland lost their March playoff against Czechia.
The 25-year-old enjoyed a strong second season at Everton, after being handed a greater role by Moyes at the start of the campaign, despite not starting a Premier League game under previous manager Sean Dyche.
The Irishman was primarily played out of position at right-back, but he excelled there and stepped up a level when moved into his preferred central role, with five appearances and just one loss.
Moyes still has James Tarkowski, Jarrad Branthwaite and Michael Keane as options in central defence, but ex-Everton centre-back Richard Dunne has called on the veteran coach to move O’Brien across.
“To get the very best out of him in the long term, he’s going to be a centre-half. It doesn’t have to be perfect straight away, he’s learned to play in the Premier League and shown he’s at the level internationally, where he's been fantastic,” Dunne told the Liverpool Echo.
“Push him inside and it’s another six months of learning his role as a centre-back in the Premier League. I think he’s more than capable of being a top performer in the Premier League.
“Now is probably the right time to get him in there. They don’t seem to be able to keep Jarrad Branthwaite fit, so having Jake in there, he’s quick, good on the turn and can make recovery runs.
“He’s a player with lots of potential. Now it’s time to let him go and put him in his main position.”