The holding midfielder's current deal is due to expire at the end of the season, but Ancelotti has stressed that Alonso remains a key figure for Madrid and hopes the 32-year-old will sign an extension before the end of the year.
"I would like Xabi Alonso to sign a new deal as my Christmas present," Ancelotti told reporters. "He is a key player for Madrid. He has a lot of experience and quality and is very important to the team.
"Xabi Alonso reminds me a bit of myself, although his passing is better and he has better technique as well."
Ancelotti then went on to make it clear that Cristiano Ronaldo remains Madrid's first-choice free kick taker, regardless of Gareth Bale's successful strike against Galatasaray.
"Cristiano remains the first choice. Bale also agrees that Ronaldo is our best bet for free kicks from close range."
Madrid is currently preparing for Saturday's Copa del Rey game against Olimpic de Xativa.