Novo Banco was established in 2014 by the Bank of Portugal to rescue assets and liabilities of Banco Espírito Santo, of which it is a subsidiary according to Bloomberg.
Final bids are due to be submitted by the end of June and while five bidders are currently in the running, one of the Chinese groups is expected to win, the Financial Times said citing people familiar with the situation.
The bank is expected to sell for more than €4 billion ($4.5 billion), with the two Chinese buyers bidding far in excess of their rivals: Spain's Santander; and American funds Apollo Global Management and Cerberus, the South China Morning Post said.
Beijing-based Anbang bought Dutch insurance company Vivat for €150 million ($166.8 million) in February, Bloomberg reported.
Fosun entered the Portuguese market last year with the purchase of insurer Fidelidade Insurance, while Apollo bought insurer Tranquilidade, another part of Espirito Santo, Reuters reported.