The Scot could include the Republic of Ireland international in his squad on Saturday after his run-out for the Under-21s, while Kevin Mirallas is closing in on full fitness
The midfielder played for over an hour for the Toffees' Under-21s side in a goalless draw against Everton last Sunday.
It was the former Manchester United man's first appearance since the 2-0 defeat to West Brom in September, but Moyes has suggested Gibson could "possibly" play a part.
"He's coming on and doing okay," The Scot told the club's official website. "He had a game for the Under-21s last week so he's making some progress.
"We need everyone back. We've had a few injuries but it's the same for every club. We want everybody back, but you've got to get them back at the right time and when you think they're ready."
|STICKING IT TO THE CANARIES|
|10/1||Everton are 10/1 with Bet365 to beat Norwich 3-0 on Saturday afternoon|
Moyes also hopes to have Belgian summer signing Kevin Mirallas back in action, though the forward is not expected to face Norwich.
He added: "He's doing okay as well.
"He's making some improvement and time helps improve it. We'll be hoping that he'll be okay."