The Toffees' winger is set to be in contention for first-team football after overcoming a succession of injuries, and could feature in the FA Cup fourth round clash against Bolton
The Belgium international has only featured once since the middle of November, due to a persistent hamstring injury forcing the former Olympiakos winger out of action and onto the treatment table.
However, Toffees' manager Moyes told reporters on Friday that Mirallas and Dutch defender John Heitinga are now both close to a return - although Monday night's Premier League clash at Southampton may come too soon for the pair.
The Scot said: "They’re getting much closer and hopefully we'll have them back, certainly if it’s not for this game [at St Mary's] it will be in the next week or two."
That means one or both could feature in Everton's FA Cup fourth round tie away to Bolton Wanderers on Saturday 26 January, and/or the home League game against West Brom on Wednesday 30 January.