The offer by Apax Partners and Bain Capital, which was announced on Wednesday by Oi, came just over a week after French group Altice launched a bid of €7.03bn for the same assets.
Like Altice's bid, the investment funds' offer excludes Portugal Telecom's business in Africa and almost €900m in debt owed by Rioforte - a company of the troubled Espirito Santo group.
A Luxembourg court had last month decided that Rioforte, the main holding company of Santo's non-financial assets, would be liquidated.
Oi and Portugal Telecom had only announced their merger just over a year ago. But the marriage has soured over Portugal Telecom's loan in April to Rioforte.
Meanwhile, Isabel dos Santos - an Angola businesswoman and daughter of the country's president - launched a separate bid to buy the holding company of Portugal Telecom which in turn owns about a quarter of Oi.
Her bid of €1.35 per share values Portugal Telecom at €1.2bn, and was dismissed by Brazil's Oi as "unacceptable" and "ill-timed".
Portugal Telecom's net profit surged 46.6% last year to €331m after it hived off its participation in a company in Macau, China.
Source: AFP, via I-Net Bridge
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