Leon Osman is in line to return to the Everton squad for the game against Birmingham.
The midfielder missed the win over Manchester City with a hamstring problem but is in line to feature in the FA Cup fourth round clash.
Moyes was also positive on the progress of four other players. He said Jack Rodwell, Dan Gosling, Victor Anichebe and Mikel Arteta were 'close' to full fitness.
Gosling and Rodwell have been missing since December with hamstring problems, while Anichebe and Arteta are almost back after eleven months on the sidelines with serious knee injuries.
Moyes said at his press conference on Friday: "We’re getting people much closer to fitness. Mikel Arteta is much closer to fitness and Victor Anichebe is much closer to fitness. Jack Rodwell and Dan Gosling – very close to it now as well.
"So I think it will not be long until we are adding those four back into the players who were available last week.
"Leon Osman looks as if he’ll be fit for the game as well, so we’re starting to get a bit more like it. We’ve still obviously got a few to come back, and the boys in Africa are still away as well so I’m looking forward to getting them all together."
Moyes was then asked directly about a potential return for Arteta and replied: "It will be close."
Tony Hibbert remains sidelined after undergoing a hernia operation, while Phil Jagielka is still recovering from his own knee injury.
Brazilian striker Jo has departed Everton for Turkey, while Joseph Yobo and Yakubu are still away with Nigeria. Yobo is also nursing a hamstring problem while in Angola for the African Cup of Nations.
Everton: Howard, Nash, Neville, Coleman, Heitinga, Distin, Baines, Fellaini, Osman, Pienaar, Bilyaletdinov, Donovan, Cahill, Saha, Vaughan, Duffy, Baxter, Forshaw, Agard.