The Spanish giants, who have spent around 180-million-pounds this summer, claim they cannot afford the midfielder.
Real wanted Alonso to provide the chances for their new strike trio of Cristiano Ronaldo, Kaka, and Karim Benzema.
But general director Jorge Valdano said: “Alonso is a priority if he fits into our budget and this doesn’t seem the case.
“Liverpool have taken up a difficult stance over Alonso. I don’t like to talk about the private details of negotiations. We are studying many alternatives,” The Sun quoted Valdano, as saying further.