* BBVA must update risks factors in documents to supervisor

* BBVA should outline savings from Sabadell deal if no merger

(Adds comment from head of Spanish supervisor in paragraph 8 and from acting Bank of Spain Governor in paragraphs 16-17)

MADRID, June 21 (Reuters) - The potential impact of an alleged spying case on Spain's second-biggest bank BBVA is difficult to estimate in terms of fines or reputational damage, the head of Spain's stock market supervisor, Rodrigo Buenaventura, said on Friday.

A Spanish High Court judge on Thursday proposed that BBVA and its former chairman stand trial for alleged bribery and disclosure of company secrets following a probe into alleged corporate spying.

A BBVA spokesperson said no criminal liability "arises for the entity from the events under investigation" and its priority had always been to cooperate fully with the courts.

The court ruling comes at a time when BBVA has launched a 12.28 billion euro ($13.12 billion) hostile takeover bid for Banco Sabadell.

BBVA was placed under investigation in July 2019 for hiring a private investigation agency allegedly run by former Police Commissioner Jose Manuel Villarejo. The case is part of a wider probe dating back to 2004 into Villarejo, who has denied wrongdoing.

"Cases like this can have repercussions on issuers, on people who have worked or who work with managers of the institutions, and it is difficult to foresee at this stage the consequences of possible sanctions or reputational consequences that the case may have on the issuer," Buenaventura said, adding that the bank had to update any risk factors.

None of the bank's current board were involved in the investigation.

Buenaventura also said it would be "highly desirable (for BBVA) to provide information on the synergies that would occur in the event of a takeover bid without a merger."

BBVA's bid is opposed by the Spanish government. Under Spanish law, the government cannot stop the process but has the final word on allowing a merger.

Earlier this week, BBVA Chairman Carlos Torres said BBVA's intention was to pursue a merger but if this was not possible it should still be able to achieve savings in areas such as technology.

BBVA would still have influence as a potentially large shareholder in Sabadell.

The bank has estimated annual cost savings from a merger at about 850 million euros before tax, spread over three years.

BBVA has already completed all the authorisation requests, such as the one for the European Central Bank, the stock market supervisor and the anti-trust competition authority.

The ECB, in close cooperation with the Bank of Spain, also has to give its authorisation on the deal.

Against that background, the acting Bank of Spain Governor Margarita Delgado on Friday said that until there was a final court judgement, there was no additional element in the situation.

"When it is final, the situation will be analysed at that time," Delgado said.

($1 = 0.9357 euros) (Reporting by Jesús Aguado; additional reporting Emma Pinedo; editing by David Latona and Jane Merriman)