LISBON--Shares in Portuguese lenders Banco BPI SA (BPI.LB) and Banco Comercial Portugues SA (BCP.LB)rose sharply Tuesday on a report that Isabel dos Santos, Africa's wealthiest woman and the second-largest shareholder in BPI, will propose that the two banks discuss a merger.

Last month, Spain's CaixaBank SA (CABK.MC) offered to buy 55.9% of BPI that it doesn't already own for EUR1.329 a share in cash, pricing a deal at up to EUR1.09 billion ($1.24 billion). BPI shares closed Monday at EUR1.36, suggesting CaixaBank will likely have to raise its offer if it wants to convince shareholders of the deal.

Ms. dos Santos, who is the daughter of Angola's president and BPI's second-largest shareholder, has remained silent on the deal. But according to Expresso newspaper, Ms. dos Santos, who owns 18.6% of BPI, isn't satisfied with the offer. Instead, she has held talks over the last few days with shareholders of Banco Comercial Portugues, including Angola's state oil company Sonangol Group, which owns close to 20%, to discuss a possible merger of the two banks, the newspaper said without citing sources.

According to Expresso, Ms. dos Santos is expected to make an announcement on her plans soon.

Shares of Banco Comercial Portugues, or BCP, were trading up 5% at EUR0.875 Tuesday, while BPI shares rose 6% to EUR1.45.

Representatives for Ms. dos Santos, BPI and BCP weren't immediately available to comment.

BPI is Portugal's No. 4 bank in terms of assets, and BCP No. 2, after state-owned Caixa Geral de Depositos SA.

-Write to Patricia Kowsmann at patricia.kowsmann@wsj.com

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