Glencore said on Friday it was in final-stage negotiations over a potential sale of its majority stake in Mopani Copper Mines to Zambia's mining investment arm ZCCM-IH.
Zambian state radio ZNBC earlier reported the government had concluded talks with Glencore, citing President Edgar Lungu.
The report did not give details about the outcome of the negotiations, but said a deal was likely to be signed next week.
Zambia's state mining investment arm ZCCM-IH has been in talks to buy Glencore's 73.1% stake in Mopani since August. Glencore's stake is held through Carlis Investments Corp, a British Virgin Islands based company.
First Quantum Minerals holds 16.9% of Mopani, with ZCCM-IH holding the remaining 10%.
Zambia's mines minister was not immediately available to confirm the report.
With Zambians heading to the polls in August, President Lungu has been working to win votes in the country's northern copper belt, where the opposition party has been making inroads.
On a visit to Mopani Copper Mines on Friday, Lungu said the government would ensure the mine continued to operate and no jobs would be lost.
Glencore's plan last year to suspend operations at Mopani due to low copper prices and Covid-19 disruptions angered the government, which said Mopani had not given enough notice and threatened to revoke the company's mining licences.