Darron Gibson could return to the Everton squad for the game at Swansea.
The January signing has been missing since the FA Cup game against Blackpool last month.
But he has been training this week after recovering from his knee ligament problem and could figure against the Swans.
But midfield pair Jack Rodwell and Seamus Coleman are likely to be missing with hamstring and thigh injuries respectively.
"Darron Gibson is improving," Moyes revealed at his Friday press conference. "We will hopefully go there with only a couple missing and maybe Darron Gibson on the way back.
"We will be very much as we were, we have got an injury to Seamus Coleman and we have an injury to Jack Rodwell."
The news of Gibson's impending return comes as a boost to Moyes, although he refused to read too much into the statistic that means the Irishman has yet to play in a game Everton have lost.
"I think we have missed him because of what he gives us," explained the Blues boss.
"I think he will improve and we will get used to him and when he played we were unbeaten in that period.
"It is difficult to weigh up exactly his importance but it may be next season before we get the best of him."