Zubizarreta admits a new centre-half signing is now a priority.
"Valencia already know our offer and we want to maintain privacy in the negotiations. Of course we have other alternatives if this falls through," he said.
"Hopefully by La Liga's start we have that centre-back position covered. If we wanted a centre-back before now, we would have signed one.
"We want someone who can put in top performances for many years and that's what we're working on.
"Signing is a centre-back is an objective for 80-90 per cent of the major European clubs so it not only depends on what we want to do - the exception is David Luiz to Paris Saint-Germain, that's the only real major movement in this regard."
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