The Papua administration wants 10 percent of the shares in the copper and gold miner, PT Freeport Indonesia, if they are divested.
The Indonesian Government has made divestment a requirement for the company.
It wants Freeport to sell 51 percent of its shares to national entities.
The Jakarta Post reports the Papua Governor, Lukas Enembe, met President Joko Widodo on Wednesday to discuss the stand-off between Freeport and the government and how it would affect the province.
Freeport Indonesia, a subsidiary of US-based Freeport McMoRan, has refused to accept a government demands that it convert its contract of work into a special mining licence.
It says such a move would annul the agreement it reached in 1991.
The multi-national has threatened to take the case to international arbitration if a mutual agreement is not met in the next few months.
Photo: MIneral Policy Institute West Papuans have long expressed frustration about the environmental destruction caused by the Freeport mine operations in Mimika regency.