Everton could welcome three players back into the squad for this weekend's visit of Newcastle.
Leighton Baines, Darron Gibson and Phil Neville have been training this week following their recent injuries.
And Moyes is hopeful that they will be in contention for Sunday's match against the Champions League-chasing Magpies.
He said at his Friday press-conference: "Hopefully they have all got a chance of being fit.
"They are all very close to fitness, most of them have trained this week, and with a bit of luck we will have very close to a full squad to pick from.
"It's great to get them back and you want them fit for all through the season. In the main we have not been too bad with injuries."
Everton will be without Jack Rodwell (hamtring) and Victor Anichebe (groin) for the clash with Alan Pardew's men.