* Head of CNMC: Too early to assess outcome of its analysis

* CNMC head Fernandez: I'm not aware of political pressure

* Cani Fernandez says divestitures can be among remedies

SANTANDER, Spain, June 18 (Reuters) - The Spanish government could set additional conditions on BBVA's 12-billion-euro ($12.85 billion) takeover bid for smaller rival Sabadell, the head of the country's antitrust watchdog said on Tuesday.

Cani Fernandez, head of the regulator, CNMC, also said that the watchdog could force the combined entity to divest in areas such as the insurance business.

The watchdog is reviewing the bid proposal and that could take at least a month, or three months if the review goes to a second phase, Fernandez told an event in Santander. Even those timelines could be extended as every time additional information is required it resets the review process, she said.

In phase three of the review, the government, which has already said it opposes the deal, has an additional two months to potentially include new conditions.

"And in that framework the government can set new conditions and it would be possible for the cabinet to impose additional conditions," she said without elaborating further.

Under Spanish law, the government has the final say on allowing a merger.

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

Fernandez said she was not aware of any political pressure regarding the bid but said it was too early for CNMC to assess the outcome of the review before undertaking a full analysis.

"We have to see how all the markets are being impacted before and after the operation and conclude accordingly," she said.

The offer is subject to BBVA acquiring more than 50.01% of Sabadell, and BBVA has said that the process could take six to eight months before formally going to shareholders.

BBVA has called an extraordinary shareholder meeting on July 5 to approve a share issue to fund the bid.

Ahead of that vote, proxy adviser Glass-Lewis on Monday recommended BBVA' shareholders to vote in favor of the capital increase, adding that if BBVA acquired the required stake, minority shareholders would have "limited influence and no strategic benefits."

BBVA's bid was rejected by Sabadell's board, prompting BBVA to launch a hostile offer directly to Sabadell's shareholders.

Fernandez said that as the two banks were not going hand in hand in the process, the situation was different from the Caixabank and Bankia merger in 2020, hinting at longer process.

"In the end, the key is how quickly we get the information to do the analysis," she said.

Conditions imposed could be similar to ones imposed on the Caixabank and Bankia merger, she said.

"In fact in the case of Caixa Bankia if I remember correctly there was some divestiture in the field of insurance, so it would not be the first time either," she said. Caixa Bankia was also required to keep a certain number of branches open.

A merged BBVA and Sabadell would have a combined market share of 21.9% in loans, putting it below Caixabank's 25% share, but it would have a much bigger market share than that in regions such as Catalonia and Valencia.

Under CNMC's regulatory framework, a compulsory review is needed when market share is above 30% of the relevant market. It also conducts a review based on availability to clients of a range of financial services and products.

($1 = 0.9336 euros) (Reporting by Jesús Aguado Editing by Andrei Khalip, Susan Fenton and Mark Potter)