Nationalizing the bank would be more of a political problem rather than an economic issue, he explained.

"It's here (in the stability of the Portuguese government) where I find risks," Diogo Teixeira dos Santos, chief executive officer at Optimize Investment Partners, told CNBC over the phone.

Portugal's Finance Minister Mario Centeno told a newspaper on Wednesday that "all options are on the table", including nationalization. Earlier last year, the government had rebuffed calls for the nationalization of the bank.

The Portuguese Central Bank and government have to find a solution for Novo Banco by August – a deadline agreed with European regulators, after previous failed attempts to recover the 4.9 billion euros ($5.2 billion) used to save the bank.

There is another pressing issue to solve in Europe's banking system: Novo Banco – a Portuguese bank that emerged from the collapse of the country's biggest lender.

Portugal is being governed by a minority-socialist led government, who enjoys parliamentary support from two leftist parties (the Left Bloc and the Communist Party). Though there are no general elections scheduled for 2017, it is clear that there are divergent views between the three parties when it comes to Novo Banco, which could shake the stability of the government.

The Left Bloc has previously mentioned that Novo Banco should be state owned, but the government continues to push for a private solution – just like the Italian government did for Monte dei Paschi, until the political turmoil forced a state intervention.

More importantly, the leftist parties want the solution to have zero impact for taxpayers. The government lent nearly 4 billion euros to the rescue of the bank – an amount that it hopes to recover with a sale. Any losses from the sale will have to be paid gradually by the other Portuguese banks.

But, even the best private option at the moment has "a potential impact on public accounts," Lisbon's central bank said Wednesday. The bank announced that an offer from Lone Star, a U.S. fund, is the best placed in ongoing negotiations.

The bank failed to specify what that impact would be and was not available for further comment.

"The intention was always to sell the bank and the Bank of Portugal started seeking suitors in 2014, but had to shelve the process in September 2015 because the three bidders did not meet price expectations," Moody's said in a banking note last October.

"Novo Banco has a very weak credit profile, and it is highly unlikely that the Resolution Fund will obtain sufficient funds to reimburse those that were injected into Novo Banco at the time the bank was created and repay the outstanding government aid," Moody's added.

More worryingly, despite efforts to fix its asset risk challenges, Portugal's third-largest lender has little chances of succeeding.

"We view that despite Novo Banco's efforts to address its asset risk challenges, Portugal's economic growth prospects (we expect GDP to grow by 1.1% in 2016 and 1.3% in 2017) are not sufficiently robust to enable a substantial decline in the bank's very large stock of problematic assets," Moody's concluded.

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