The Spain international is among a host of players who have been linked with a move to the Bernabeu following Perez's re-election.
Real are desperate to address the European and domestic dominance of fierce rivals Barcelona in 2008/09, who became the first Spanish side to complete the Treble.
Perez has identified former Real Sociedad star Alonso's qualities and has hinted that he could approach Reds manager Rafa Benitez.
"As a fan, I would say that Xabi is a great player. I think he is the best passer of the ball in Europe," he told the Radio Television Espanola.
"I would be happy [to have him], but I cannot talk about the player without having spoken first to Rafa Benitez, as he is the one who needs to know that we are interested in his player."