Antolin Alcaraz is in line to be fit for the start of the season.
The defender, a summer free transfer arrival, isn't part of the Everton squad in the USA and has remained at home to nurse a hamstring problem.
But boss Roberto Martinez told evertontv the problem wasn't too serious and is looking forward to welcoming the Paraguayan back to the main training group before the Premier League kicks off on 17 August.
He said: "Antolin will be out for a couple of weeks, I wouldn't expect any more than that. It was more beneficial for him to work at Finch Farm so we can make sure we get him fully fit as soon as we can."
And Magaye Gueye, another injury absentee from the America tour party, could be back even sooner after picking up a knock against Accrington.
"Magaye is recovering very well. I would say he is in the last 10 days of his individual treatment plan and he should be able to join the group very quickly. It's a shame he has missed the trip but it is to his benefit to stay at Finch Farm.
"It's a shame they can't both be with us but we send them good wishes - especially Antolin on his birthday."