By 2200 GMT Rioforte is supposed to repay 847 million euros ($1.16 billion) in maturing debt to the country's largest telecom services provider, Portugal Telecom, currently in the throes of a tie-up with Brazil's Grupo Oi, which is likely to amend the terms of the deal in the event of a default.
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The sources would not comment on how a creditor protection filing could affect the payment deadline. They said negotiations between Rioforte and PT were still going on.
Rioforte would not comment.
Concerns surrounding the Espirito Santo banking clan, who founded Portugal's biggest listed bank, Banco Espirito Santo, have flared since an audit of a family holding company that owns Rioforte found a "serious financial situation" there. Last week the worries sent European markets into turmoil.
Further evidence of the family's financial difficulties came late on Monday, when a group company sold a 5 percent stake in BES, set up more than a century ago, at a deeply discounted price because it had to meet a margin call.
The sale helped push BES shares 20 percent lower at one point on Tuesday to record lows just above the 0.34 euro price at which the Espirito Santo Financial Group (ESFG) sold the 5 percent stake. The shares were last 10 percent lower.
"The sale by ESFG at a brutal discount shows they are jumping ship," said Jose Novo, a trader at Orey iTrade brokers.
"The stake sale was a great pressure factor as they put a sort of a target price into people's heads, but it would have been difficult to sell a big block of shares otherwise in the market," said Andre Rodrigues, an analyst at Caixa BI.
Yields on BES debt kept climbing on fears bondholders would bear the cost if the bank ran into difficulty, reaching 11.7 percent on 10-year bonds, up from 10.6 percent on Monday and more than double where they stood a month ago.
Last week, news emerged that an Espirito Santo family holding company had failed to meet debt payments in full and on time.
"There are reports and expectations that holding companies of the Espirito Santo group could at any moment file for protection, Portugal Telecom being just one of the creditors who would be affected," said Rodrigues.
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PT's Brazilian merger partner is watching the debt payment carefully.
A source close to the deal told Reuters on Tuesday that some large shareholders in Grupo Oi could sue Portugal Telecom if the debt investment ends up in default.
Neither Portugal Telecom nor anybody at the Espirito Santo family has commented on the payment, and they are not expected to until after markets close.
The concerns have driven shares in Portugal Telecom down about a third in the past few weeks and were around 2 percent lower on Tuesday.
Efforts to distance BES from the founding family accelerated on Monday after the Bank of Portugal ordered that a new, independent management team take over immediately.