MADRID, May 7 (Reuters) - Shares in Spanish bank BBVA rose as much as 1.9% on Tuesday morning after Sabadell rejected what it described as an unsolicited takeover proposal from BBVA.

At 0805 GMT, shares in BBVA, Spain's second-biggest lender by market value, were up 1.5%, while those of number four lender Sabadell were down 1.7%.

On Monday, Sabadell said its board believed BBVA's proposal significantly undervalued its potential and growth prospects. BBVA said it regretted Sabadell board's decision, without giving any hint of its next move.

BBVA could now walk away, raise its offer, or launch a hostile takeover bid. A spokesperson declined to comment.

Spanish broker Alantra said it did not expect BBVA to improve its offer or go hostile.

"We rule out that BBVA will go hostile (...) given that the management will destroy its track record of financial discipline and that around 50% of Sabadell shareholders are retail investors, which would largely follow the board's decision in any case," it said.

The broker also said it believed BBVA would not switch into a cash bid as it was proposing a friendly merger, and paying cash would be inconsistent with that.

RBC Capital, however, said BBVA would likely have some wiggle room on price, and "Sabadell has probably not fully closed the door to future negotiations, although the two parties currently seem a long way away from finding middle ground".

Last week, BBVA proposed offering one newly issued BBVA share for each 4.83 Sabadell share, a 30% premium to Sabadell's closing price on April 29 and valuing it at about 12 billion euros ($12.9 billion).

Since then, Sabadell's shares have risen about 8.8%, while BBVA's have fallen 9.7%, reducing the value of the proposal to around 11 billion euros.

($1 = 0.9291 euros)

(Reporting by Jesús Aguado; Additional reporting by Andrés González; Editing by David Latona and Mark Potter)