Officials from both clubs met at Las Rozas on Friday to discuss the issue, which has been a major bone of contention in Spain ever since Real Madrid declared that the Santiago Bernabeu was not an option for the tournament decider.
However, Barca and Bilbao remain at loggerheads over not only the venue, but also the date of the game, according to AS.
The Catalans want the final staged on May 25 at the Vicente Calderon in Madrid, while their Basque rivals are pushing for a meeting at the Cartuja in Seville five days earlier.
As a result of the standoff, the RFEF will now decide the venue when its board of directors meet next Tuesday.
AS claims that Mestalla is now back on the table and could be selected as a compromise.
Barca and Bilbao's meeting in the 2009 Copa del Rey final was staged at Mestalla, a game marred by the booing of the Spanish national anthem by fans from both sides.
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