A government company currently owns about one-third of Centerra, the Toronto-based company that operates the mine where protesters blockaded a key access road and cut power last week.
Centerra says the two sides are considering a swap to shift ownership of Kumtor from the company to a joint venture with the government.
It says the government's Kyrgyzaltyn JSC would exchange its stake in Centerra for a stake of equivalent value in the new joint venture.
Centerra says it expects a "constructive dialogue" but added there's no assurance that the two sides can reach an agreement.
In addition to Kumtor, Centerra owns the Boroo mine and Gatsuurt development property in Mongolia.