Reports in Spain have strongly linked 34-year-old Pirlo with a move to the Bernabeu with the Italy international set to become a free agent in the summer of 2014.
"I speak to Pirlo often. And I am happy that he received an ovation from the Bernabeu crowd (in Juve's 2-1 Champions League defeat at Real Madrid on October 23).
"He got more applause that night than Real has received during this period."
Ancelotti insisted Real have no intention of letting Alonso leave.
The Spain international has been a key man since joining the club from Liverpool in the summer of 2009.
Alonso is under contract with Los Merengues until June 2014 but is expected to sign a new deal before the end of the year.
"Xabi is a crucial player for Real Madrid," Ancelotti said. "He was injured recently but he has recovered and for us he is a fundamental player.
"There are no players like him, the only one that could be considered of his level is Pirlo."
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