Valencia and Barcelona - F1’s two Spanish race hosts - are now in "informal contact" about alternating a single annual date on future calendars.
According to the Spanish-language news agencies EP and EFE, it was the Valencian government’s vice-president Jose Ciscar who made the comment last Friday.
A day earlier, the president Alberto Fabra confirmed he had a meeting in London last week with F1 chief executive Bernie Ecclestone, asking to keep the Spanish port city on the calendar but with "different conditions".
Ciscar said Fabra passed on to Ecclestone the "economic difficulties" being faced within Spain, and the need for "major events like formula one" to become "less burdensome" to the region’s coffers.
He said there would be "more news in the coming weeks".
Ecclestone, meanwhile, admitted to Austria’s Salzburger Nachrichten newspaper: "I have tried to get Barcelona and Valencia to alternate, but the Spaniards have not wanted to discuss it.
"We should not have two races there," he added.