President Hichilema, who was on his way to France for an international finance summit, told a news conference during a visit to the Rwandan capital Kigali that an agreement on restructuring Zambia's debt was expected.
"The framework that we should agree on in the next few days, and the presence of others (leaders) show our urgency to conclude," he said.
He hoped his presence in France, alongside French President Emmanuel Macron and the Chinese Premier Li Qiang, would help speed up the process.
"The three of us should stand side by side," he said.
"It is our desire to conclude the Zambia debt restructuring, ...to see closure," said Hichilema. It's been hanging on for too long".
He described the debt as a "python crippling us in the neck, the ribs and the legs."
The United States has accused Zambia's biggest creditor China, of dragging its feet. Of Zambia's total debt, China is owed a third.
A senior U.S. Treasury official welcomed "progress made on Zambia and hope an agreement on official bilateral creditors is imminent."
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 Paris Club, an informal group of official creditors whose role is to find solutions for countries having trouble repaying their debt, began meeting Wednesday, ahead of the summit in Paris which aims to find ways to reform global financing for a new era shaped by climate change.