Fosun International and privately owned Anbang Insurance Group are believed to be still in the running for Novo Banco, the successor to Portuguese lender Banco Espirito Santo after a state rescue last year.
The Bank of Portugal had selected five of the seven financial institutions that had made non-binding bids for Novo Banco, and will accept binding offers until the end of June.
The central bank said that in this third phase of the sale the chosen five would get access to more detailed information about Novo Banco and would be able to do "due diligence" checks on its worth. It did not name the institutions.
In a research note last month, BBVA analysts estimated Novo Banco could fetch between €4.3 billion (HK$36 billion) and €4.8 billion.
Sources and the media have said Santander, Fosun, Anbang and US investment fund Apollo Global Management were still in the race, while Portugal's Banco BPI and Bank of China were most likely out.
Another contender cited is New York-based investment firm Cerberus Capital Management. Only Santander and BPI have publicly confirmed their bids.