Negotiations on the form in which Cuba will pay the remaining debt are ongoing, the diplomats said, as even $320 million per year represents a large sum for the cash-strapped country, which has labored under a U.S. economic embargo for decades.
Cuba's total export earnings are around $18 billion, including tourism and medical and educational services.
Neither Cuba nor Russia has made any official comment on the debt agreement. Cuban officials were not immediately available for comment.
Cuba defaulted on its debt in the late 1980s but recently has been trying to restructure the old debts to improve its international credibility.
Russian Prime Minister Dmitry Medvedev, during a visit to Cuba in February, signed a general agreement to work out a formula and settle the old debt by next year. The decision rankled other countries grouped in the Paris Club of creditor nations because it broke ranks with the collective approach of the organization.
PARIS CLUB CONTACTS
The Paris Club is an informal group of creditor governments including Canada, France, Germany, Japan, Russia, the United Kingdom and the United States as well as a number of smaller European nations.
The Paris Club reported that Cuba owed its members $35 billion at the close of 2012, now estimated at around $37 billion, which would leave the island owing $5 billion to $6 billion of non-Soviet debt to the club's members.
The organization has a Cuba working group, which does not include the United States.
Russia pledged to work with Cuba towards reaching an agreement with the Paris Club as part of the October settlement, one Russian diplomat said.
"The Paris Club should be grateful as it removes a huge amount of money from the table and makes an eventual agreement more likely," he said.
While some Paris Club members clearly preferred a united front, one European diplomat said Russia's help in settling Paris Club debt could prove important and that a reduced debt would indeed be more easily negotiable.
Since the Medvedev visit, the Paris Club has put out feelers to the Cubans and a few months ago two representatives traveled to the Caribbean island to meet with the central bank, the first such visit in over a decade.
Unlike the International Monetary Fund and World Bank, from which Cuba is excluded under the longstanding U.S. trade embargo, the Paris Club does not issue multilateral loans.
Cuba releases very little information about its foreign debt.
Last month the government reported its "active" foreign debt, accumulated after it declared a default in the late 1980s, as $13.6 billion in 2010. The government no longer reports its "passive" debt from before the default and estimated at around $8 billion.