The 31-year-old Spain international missed June's Confederations Cup to have surgery on a groin problem and then broke a bone in his foot in training in August.
"He is available," Ancelotti told a news conference. "He is training with the team and I think tomorrow he will start on the bench and I will try to give him minutes during the game.
"He has all the necessary quality to help the team play better. He has experience, passing quality and a good defensive attitude. He is a very important player for us."
A consummate passer, Alonso has been a key performer for Real in his central midfield role since joining in 2009 and they have struggled to exert the same level of control over opponents in his absence.
Third-placed Real are six points behind leaders Barcelona, who play at Celta Vigo later on Tuesday, after they were beaten 2-1 by their arch rivals at the Nou Camp on Saturday.
Atletico Madrid are second, five clear of Real and a point behind Barca ahead of their match at Granada on Thursday.