The Lausanne-based private bank said in a letter to clients there were potential buyers willing to pay for the illiquid debt at 2 percent of face value, the source said.

The price would imply a 98 percent loss for investors in the holding company, which is part of Portugal's Espirito Santo family's crumbling web of businesses.

This marks one of the first indications of what creditors of the Espirito Santo group of companies might receive.

In early July, the Swiss private bank became the first Espirito Santo group entity to acknowledge that its clients had not been reimbursed on debt issued by Espirito Santo International.

This holding company has around 630 million euros (500.59 million British pound) in tradable debt instruments in the market, including commercial paper and bonds, while its total debt exceeds 6 billion euros.

Portuguese financial regulators knew in January about deep financial problems at Espirito Santo International, which continued to borrow heavily in the months that followed.

The family empire issued 5 billion euros of new debt in the first half of 2014, according to people familiar with the matter, just as the clan’s businesses were running into trouble.

Requests for creditor protection by family holdings Espirito Santo International, Espirito Santo Financial Group and Rioforte in July ultimately led to a state-organised 4.9 billion euro rescue of Portugal's largest listed lender Banco Espirito Santo on Aug. 3 related to its exposure to the Espirito Santo family businesses.

The source said the information provided by Banque Privee Espirito Santo did not constitute an offer to buy nor a recommendation to sell the debt.

"BPES only transmitted the information supplied by market players in fulfilling its duty to the clients to keep them informed and to track the situation at ESI," the source said. "The information is that there is buying interest for ESI debt at 2 percent of face value."

The source said debt issued by other troubled Espirito Santo holdings Rioforte and ESFIL that is held by clients was likely to attract higher offers since they hold their own assets.

Espirito Santo International is the Espirito Santo family's Luxembourg-based umbrella holding company that has been under creditor protection since July after failing to meet its debt obligations.

BPES is owned by Espirito Santo Financial Group , which in July sold part of the bank to CBH Compagnie Bancaire Helvetique. BPES did not disclose any details on the debt held by its clients.

(Reporting By Andrei Khalip. Editing by Axel Bugge and Jane Merriman)

By Andrei Khalip