As yet, Real have failed to meet Liverpool's asking price – £30 million up front with a further £3 million dependent on his success at the Bernabeu – with the club's president Florentino Perez angry at being held to ransom over a player he does not see as a marketing and merchandise investment. Real have previously intimated they are only prepared to pay a total of £26 million.
Talks between the clubs had reached a stalemate but the dynamic of the negotiations was changed by Alonso's decision last week to hand in a formal transfer request.
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Madrid contacted Liverpool over the weekend to request the meeting on Sunday morning in the Juan Carlos I hotel in the Catalan capital, where Liverpool faced Espanyol as their pre-season preparations continue.
Perez, under pressure from his coach Manuel Pellegrini and technical director Jorge Valdano, is likely to submit an improved offer – his initial reaction to Alonso's transfer request was to suggest that Madrid would have to pay less than they had previously offered – while Liverpool may be prepared to lower their price, thanks to manager Rafael Benitez's desire to have the saga over as soon as possible to give him time to seek replacements.
Any agreement is likely to be closer to the English side's valuation, rather than Madrid's.
Sources at Anfield insist the outcome of the talks is far from certain and remain unwilling to put a timescale on a definitive conclusion, though it has been suggested in Spain that Alonso could be a Real player as early as Tuesday morning, a belief bolstered by Real's increasing attempts to trim their squad.
Eight players have arrived at the Bernabeu since Perez started his second tenure at the club, while just four have left, giving Pellegrini a squad of 29 players, when Spanish league rules dictate only 25 can be registered.
Real this weekend sold Gabriel Heinze to Marseille and on Sunday agreed a £15 million fee with Inter Milan for the sale of Wesley Sneijder, the Dutch international, while his compatriot Rafael van der Vaart has also revealed that he will not stay at the club.