The "Paris Club," an informal group of official creditors, will meet Wednesday, a day before an international summit, also in the French capital, which aims to find ways to reform global financing for a new era shaped by climate change.
"I think we have done our work at a technical level, now it's a question of ironing out the last details and being ready to make an offer to Zambia," the source, who spoke on condition of anonymity, said.
"We are hopeful we can make an announcement during the summit," the source added, "We are close to the finish line."
"The president of Zambia will be there, the prime minister of China will be there, numbers of creditors from the Paris Club will be there, so hopefully we can be in a position to offer a debt treatment to Zambia."
Zambian President Hakainde Hichilema told AFP in an interview last month that the debt is "like a python around our necks, ribs and legs".
In April, International Monetary Fund Managing Director Kristalina Georgieva said that she had been given fresh assurances during a trip to Beijing that China supported a debt restructuring program for Zambia.
Negotiations on restructuring Zambia's debt - a key step towards unblocking the IMF's aid plan for the country - have been under way for two years.
The process is part of the G20's common framework for the restructuring of debt of the poorest nations.