The world's oldest bank's woes have raised concerns over the eurozone's third-largest economy, particularly in the aftermath of prime minister Matteo Renzi's resignation after a crushing referendum defeat.
The bank's prospects appeared somewhat less alarming on Sunday however, after Italian President Sergio Mattarella asked Renzi's ally Paolo Gentiloni to form a new government.
BMPS's stock tumbled on Friday over reports that the European Central Bank had denied it more time to raise the cash it needed to avoid being wound down, triggering speculation it would be forced to seek a government bailout.
The bank - seen as the weak link in Italy's economy - had asked to be given until January 20th to avoid collapse.
The request was reportedly refused, with the ECB's board believed to have ruled that two weeks of extra time would be of little use in turning around the historic bank.
In a statement published late on Sunday after a board meeting in Milan, BMPS said it had "decided to go ahead" with plans to seek a market-led rescue by December 31st.
The bank had initially announced its plan to seek a private sector-led rescue in July.
The bank, whose stock has fallen more than 80 percent this year, plans the sale of 27.6 billion euros ($29 billion) in non-performing loans. It also aims for a capital injection of up to five billion euros.
BMPS has already collected more than a billion euros by converting bonds into shares - but it still has four billion more to go before it is in the clear.
According to reports in the Italian press, up to two billion euros could be raised by allowing private investors to convert bonds into shares.
Though it remains unclear whether the bank's plan will actually work, BMPS appeared Sunday to have avoided the worst-case scenario.
Italian media reports say the Qatar Investment Authority - the Gulf nation's state-owned holding company - may be willing to contribute another billion euros.
"Qatar is ready and willing to contribute the sum that was mentioned," a source close to the BMPS board reportedly said.
BMPS's prospects appeared more favourable on Sunday, particularly after Gentiloni was named prime minister.
Renzi's foreign minister, Gentiloni, 62, was asked to form a new centre-left government that will guide Italy to elections due by February 2018.
However opposition parties demanded an immediate vote, claiming Renzi would continue to pull the strings from behind the scenes.
Meanwhile Italian media said the ECB is seeking to open an investigation into the information leak that saw reports published on its refusal of BMPS's request for more time --even though the bank's decision was not yet final, and had not been officially communicated.
Italy's political crisis has added to deep worries about the failure of the country's banking sector - which features no fewer than 700 banks - to make meaningful progress towards consolidation.
Non-performing loans on their books amount to a combined 360 billion euros, roughly a third of the eurozone's total bad debt.
By Celine Cornu