Since its completion in 2009 — a year after a decade-long construction boom turned to bust, plunging Spain into its worst recession in recent memory — the airport has been held up as one of the worst excesses of the country's go-go years.
It is seen as a prime example of the reckless ambition that drove local and regional governments to build museums, racetracks, sports arenas and oversized transport hubs up and down the country in the period leading up to the financial crisis.
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A spokeswoman for the local court in Ciudad Real that handled the auction said the bid had come from a Chinese company called Tzaneen International. But she stressed it was not clear whether the airport would be auctioned off to Tzaneen as the bid was significantly below the 40 million value set by the court.
The deadline has been extended until September 15 in the hope of attracting higher offers.
Ciudad Real, a provincial capital of just 75,000 inhabitants, was always seen as a peculiar choice to build a major airport. The city is more than two hours' drive south of Madrid, the Spanish capital, with little potential for tourism and only negligible commercial activity.
The airport was originally named after Don Quixote, the hero of Miguel de Cervantes's famous novel. The name was quickly changed, but the association with the delusional knight would prove apt: even when it was operational, the airport never handled more than a handful of flights a week.
Operator CR Aeropuertos went bankrupt in 2010, and all attempts to extract value from the remaining assets have run into problems.
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The airport and surrounding grounds were initially put up for auction in 2013, with an asking price of 100 million euros but no buyer was found.
The process was restarted earlier this year with a target price of 80 million euros, but a decision to go ahead with the sale was delayed repeatedly. The court then decided to split the assets into two packages, auctioning off the buildings and runway separately from the surrounding land.
If no further bid is made by September 15, the court will either cancel the auction again or sell it to Tzaneen. A sale at such a low price would crystallise what is certain to be one of the most spectacular financial losses made over the course of Spain's boom-and-bust years.
Spain's other famous ghost airport, a 150 million euros project in Castellon, is still in operation, and attracted attention earlier this year when Ryanair announced it was establishing a base there.
Cities such as Valencia and Santiago de Compostela, meanwhile, embarked on ambitious museum projects during the boom years that are now widely regarded as costly follies.