The club has been hit hard by the coronavirus outbreak which has decimated its already fragile finances.
Last week, club captain Dani Parejo and Francis Coquelin were sold to rivals Villarreal for a combined price of just €15m - sales which prompted fans to plan protests outside the Mestalla.
Then, just a few days later, it was reported that the players were being given 'promise letters' of wages instead of being paid their usual salaries.
Club president Anil Murthy said: "We must lower salaries, which means selling players with two years or less on their contract and high salaries. Additionally, some are ageing and prone to injury."
Now, according to Marca, they could be preparing to cash in on Rodrigo, who only last summer was linked with a big money move to Atletico Madrid, while Barcelona were interested in a deal in January before they signed Martin Braithwaite.
With the asking price now dow from €60m to €25m, various clubs have been linked with a potential deal including Marcelo Bielsa's Leeds who gained promotion to the Premier League after winning the English Championship.
Rodrigo has played in England previously, having featured for Bolton in the 2010/2011 campaign.