The 31-time la Liga winners, bankrolled by returning president Florentino Perez, have already splashed out more than €200 million on Cristiano Ronaldo, Kaka, Karim Benzema and Raul Albiol during the close season.
And the Bernabeu outfit, desperate to reclaim supremacy in Spain following arch rivals Barcelona's treble-winning exploits last season, had no intention to stop spending, with Liverpool midfielder Alonso and Bayern Munich middle-man Ribery also on the club's expensive wish-list.
However, with Anfield boss Rafael Benitez insistent on receiving around £35 million for his prize asset, and Bayern adament that Ribery is not for sale at any price, Real appear resigned to defeat and may now have to wait until at least January to renew their interest.
"Rumours have abounded this week," sporting director Pardeza told Cadena SER.
"Xabi Alonso is a great player and we can't deny that this team would greatly benefit from his work, but it looks like the situation may not end up well for us.
"We'll nevertheless keep fighting for him and hope negotiations become reasonable again.
"Bayern Munich haven't even shown interest in transferring Ribery.
"It doesn't seem to be reasonable to keep insisting when so much money is asked for a player."
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