The Tibetan Women's Association (TWA) said it would like to contest a recent statement made by Chinese foreign ministry Spokesman Hong Lei that "The door for contact is open but I want to stress that we only talk with the personal envoy of the Dalai (Lama) and we will only talk about the future of the Dalai not anything about Tibet".
"We are very much in hope that the new prime minister will consider Tibet during this meeting," the association said in a statement.
It appealed to the prime minister to "urge China to respond to the negotiations extended by the exile-Tibetan leadership".
Wang Yi arrives Sunday for a two-day visit during which he will meet Modi and External Affairs Minister Sushma Swaraj.
The association also sought to highlight the spate of self-immolations in Tibet, which number 131.
"The self-immolators have repeatedly called for the return of his holiness the Dalai Lama and freedom in Tibet. Leaders across the world and Tibetans in exile have made numerous appeals to China to examine its policies.
"China, however, instead of responding to these appeals, has further intensified the suppression of Tibetans in Tibet. Moreover, we are now seeing a new level of repression in the punishment of not only the families of the self-immolators, but the entire community.
"We believe that only coordinated and swift diplomatic action can stop this crisis. We thereby request you to kindly highlight the current crisis in Tibet during your meeting with the foreign minister of China.
It said it was "deeply grateful" to the Indian government "for all the support and help" and for providing the requisite security for the Dalai Lama.
The invitation to Lobsang Sangay, political head of the Tibetan government in exile, at the swearing-in ceremony of Prime Minister Narendra Modi is believed to have not gone down well with the Chinese government.
The TWA is the second largest Tibetan NGO based in exile in India and the only women's NGO in Tibetan history. It is a 17,000 member organisation with 56 chapters in four continents - Asia, US, Europe and Australia.