MADRID, May 2 (Reuters) - Shares in Spanish bank Sabadell rose around 5% on Thursday, adding to gains since bigger rival BBVA announced a merger proposal this week, but still far off the premium offered as the market assessed the viability of the all-share deal.

Sabadell shares have risen by over 8% since Monday's closing price. BBVA announced the merger talks on Tuesday, aiming for a deal that would create a Spanish bank with assets of nearly 1 trillion euros ($1.07 trillion) and a market value close to Santander's.

Under the terms of the proposal disclosed on Wednesday, which was a market holiday, BBVA offered a premium of 30% over Monday's closing price of 1.7375.

This valued Sabadell shares at 2.25875 euros, under the proposed exchange ratio of 1 new BBVA for every 4.83 Banco Sabadell shares, giving the smaller bank a market value of 12.23 billion euros ($12.84 billion).

Against, Tuesday's closing price, the premium was 17% as analysts.

Analysts at Renta 4 said Sabadell may not like the shares-only proposal, which is the lenders' second attempt at a merger after talks were called off in November 2020 over disagreements on the terms.

"We see no possibility of an improved offer from BBVA if Sabadell rejects the proposal. If BBVA were willing to pay part of the transaction in cash, it could be a move that would pave the way for closing the merger," Renta 4 analysts said.

BBVA's own shares slipped by 2.7% on Thursday, and were down by over 9% from Monday's close.

In a note, Deutsche Bank analysts saw the premium as "attractive enough", but not "outstanding".

"We do not see much value added for BBVA in this deal, in spite of making strategic sense. It looks difficult to reach that 20% return on investment announced," they added.

Analysts also expect the power distribution in the merged bank to be a relevant issue in reaching an agreement.

According to BBVA's proposal, three Sabadell board members, chosen by mutual agreement, would join BBVA's board as non-executive directors.

BBVA said it was ready to "move forward immediately with the transaction". In response, Sabadell said it was up to its board to assess the offer.

In its letter to Sabadell's board sent to the supervisor, BBVA Chairman Carlos Torres said: "we would therefore be grateful if you could give us your assessment of this proposal as soon as possible so that, if we have your support, we can submit a joint merger project without delay to our respective Boards of Directors for their final approval."

The potential merger follows a period of consolidation in Spain's banking sector. The country now has 10 banks, down from 55 before the 2008 global financial crisis.

Morningstar equity analyst Johann Scholtz estimated that the merger would boost BBVA's share of Spain's deposits market to around 23% from 15% now, just behind Caixabank at around 25% and ahead of third-placed Santander at 22%.

($1 = 0.9349 euros) (Reporting by Matteo Allievi; Editing by Andrei Khalip, Jesús Aguado and Susan Fenton)