Everton will be without Marouane Fellaini for Sunday's game at QPR.
The midfielder misses out with the knee injury which saw him withdraw from the Belgium squad earlier this month.
Fellaini's injury isn't too serious and he could be back for the Merseyside derby in eight days' time.
Moyes said: "Marouane has a bit of a knee injury, but we don't think it's too bad and hopefully he'll be okay. Not for this weekend, but then we'll see how he is.
Moyes also revealed that Darron Gibson had been able to complete some training as he recovers from a thigh injury.
"The progress is slow," said the Everton boss. "He's got a tendon problem in his thigh. He's been doing quite a bit of training but we're not quite sure where he is at yet.
"Tony Hibbert's not there yet. He's started a little bit of training so we're hoping by next week he'll be okay."
The Blues boss also revealed some 'knocks and bruises' after the international break but remained confident they wouldn't be a problem for this weekend's clash.
New signing Thomas Hitzlsperger is waiting for international clearance but Moyes indicated the acquisition was largely to allow him to take a closer look at the German.
The Scot explained: "What we're going to do is see how he is first. We're not saying what he's going to bring to us - he may even come here and not play.
"We just want a longer period to have a look at him, make sure he's fit and see if he can offer us something."