Midfielder Morgan Schneiderlin is set to return to full training on Tuesday but Everton's New Year's trip to champions Manchester City will come too soon for the Frenchman.
Schneiderlin has been nursing a calf problem since Everton's 3-1 win over Chelsea in early December, however Ancelotti is hopeful the 30-year-old will now be in contention for the weekend's FA Cup clash with Liverpool.
Ancelotti will head into the meeting with Manchester City having the same squad to choose from as that which earned a 2-1 victory at Newcastle United on Saturday, with Alex Iwobi continuing to recover from a hamstring issue.
Midfielders Jean-Philippe Gbamin and Andre Gomes remain long-term absentees but Ancelotti confirmed both are progressing well with their rehabilitation from quadriceps and ankle injuries respectively.
Speaking at his pre-match press conference on Tuesday, Ancelotti said: "The injured players [for the Manchester City game] are the same.
"We have almost close to recovery Morgan Schneiderlin. He will start to train with the team today and I think he will be available for the game on Sunday.
"The others, we didn't have any problems in these two days [since Newcastle] and that was good.
"Andre Gomes and Gbamin need time to recover but everything is going well with them."
David Silva and John Stones (thigh) both face late fitness tests for Manchester City, who have goalkeeper Ederson back from a one-match suspension.
Definitely out for the champions are Aymeric Laporte and Leroy Sane, with both recovering from long-term knee injuries.