The Spain international is in the final year of his contract at the Liga giants, meaning he is free to discuss a move to another club in January.
Alonso has been linked with several suitors ahead of the opening of the transfer window, with former club Liverpool touted as a possibility.
Ancelotti, though, has always remained adamant the 32-year-old is vital to his plans at Real, but also believes the squad has enough talent to cope with his absence should he decide to depart the Spanish capital.
"I don't need to convince anyone of the importance of him to the team," Ancelotti said.
"He has experience, quality and is one of the best midfielders in the world and that is why we are pushing for him to stay.
"All I can do is count on him until the summer and make the most of him while he is here. He gives more confidence to the team but we have other important players and we have also got good results without him."
Ancelotti is preparing his players for a trip to managerless Valencia on Sunday and is seeking a swift response after a disappointing 2-2 draw at Osasuna in their last league outing last Saturday.
The fixture marks Real's last match before the mid-season break in Spain and the Italian is hopeful of finishing the year on a high.
"This is a big game for us and we are up against a team who are changing coach so the players will be extra motivated to show what they can do," he added.
"They are likely to be more motivated but we want to finish the year well, perform well and take home the points."
