Real Madrid coach Pellegrini desperate for Perez to sign Liverpool's Xabi
The Daily Mail says Pellegrini and the club's dealmaker Jorge Valdano have urged club president Florentino Perez to find the funds to sign Alonso.
Perez believes the Liverpool midfielder is still overpriced, even though reports in Spain say his asking price has dropped as low as £26.5million after starting at more than £40m just a few weeks ago.
Alonso is seen as a one of a dying breed of versatile attacking midfielders and Pellegrini and Valdano believe the 27-year-old is fundamental to their plans.
Madrid are increasingly frustrated by their inability to cut their bloated squad.
Perez is reluctant to pay more than £23.5m up front with further fees dependent on appearances and success in the Champions League.