The Germany international suffered an anterior cruciate ligament tear during his country's 1-1 draw with Italy in November, making him a doubt for the FIFA World Cup in Brazil.
Germany team doctor Hans-Wilhelm Muller-Wohlfahrt stated at the time that Khedira's World Cup hopes were not over, and now club boss Ancelotti claims that the 26-year-old could play a part in the latter stages of Real's campaign.
"His recovery work is going very well. He has started running after three and a half months," Ancelotti explained.
"Everything is going well and I think that in 15 or 20 days he can be in Madrid working with the team. We hope he can play before the end of the season."
Ancelotti's side remain in the running for the treble, having moved top of La Liga, booked their place in the Copa del Rey final and won 6-1 against Schalke in the first leg of their UEFA Champions League tie.
Despite having the likes of Luka Modric, Xabi Alonso, Isco and Asier Illarramendi available to choose from in midfield, Ancelotti is eager for Khedira to return.
"He's a player this team needs, because he's very important," the Italian continued.
"Making a decision without Khedira isn't easy. With Khedira it'll be even harder."
