The European champions made a second improved offer of £7.5m for the 24-year-old centre-half on Tuesday, having had a £6m bid rejected earlier this summer. Zaragoza, however, have again underlined their determination to keep Milito by pricing him out of a move to Anfield.
The sporting director of Zaragoza, Miguel Pardeza, said: "There have been contacts with Liverpool and they have made an offer for Milito. But the player is not for sale, he is fundamental for us and we want to keep him."
Liverpool will not countenance a deal which, with wages included, would be worth £20m despite the player's impressive recovery from a knee injury that curtailed a move to Real Madrid from Independiente two years ago and Rafael Benitez's desire to bolster his defence.
Milito is currently on holiday in his native Argentina considering Zaragoza's offer of a new five-year contract, although he could revive the deal if he refuses the offer from the Spanish club and demands a transfer.
"If Liverpool make a concrete offer then it would be very difficult to say no," he said. "I am happy at Zaragoza but it is not every day the champions of Europe are interested in you."
Liverpool have offered the defender Sami Hyypia a new two-year contract to replace his current deal, which has only 12 months left to run, and handed the Norwegian international John Arne Riise a pay rise.
One player who will be moving from La Liga to Merseyside is Mikel Arteta, who is to finally seal a permanent transfer to Everton after reducing his wage demands.
The former Barcelona and Rangers midfielder spent the second half of last season on loan at Goodison Park with a view to a £2.8m switch only for his original request of £33,000 a week to stall the deal. Arteta, 23, has now fallen into line with salary cap, which will hand the Everton manager, David Moyes, a much-needed transfer fillip having missed out on Craig Bellamy, Scott Parker, Emre, Mikaël Forssell and Mohamed Sissoko this summer.
The chief executive at Everton, Keith Wyness, said: "Talks with both Real Sociedad and Mikel Arteta have gone well and are continuing. We are hopeful of reaching a satisfactory conclusion within the next 48 hours or so."
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