Bopanna and Qureshi, the "Indo-Pak Express" who hope their doubles partnership can help their bitterly divided countries, said the initiative was now backed by the world tennis body and an international peace group.
The pair are pushing for a match using a net strung across the famed Wagah border crossing, as part of their "Stop War Start Tennis" campaign. India and Pakistan have had three wars since the end of British colonial rule.
Qureshi said the International Tennis Federation (ITF) had thrown its support behind the scheme, along with Peace and Sport, a non-governmental organisation run by Prince Albert of Monaco.
"A lot of good things have been achieved, the ITF is now supporting this, Peace and Sport is also supporting this," Qureshi said. "The letters have gone to both the prime minister and president of both countries.
"It is a political issue and there are a lot of security concerns, so we are just hoping that the governments will give us the green light so we can play that match on the border."
Qureshi and Bopanna, who were finalists at last year's US Open, are confident of a positive response from their respective governments.
"Things are going in the right direction," Qureshi said.
"Last year, at the US Open, both the UN Ambassadors for Pakistan and India came and watched our matches, which was a huge thing and they are supporting the cause as well.
"Things are going in the right direction, we just have to keep playing our matches and get more and more publicity on the bigger occasions.
"Hopefully it will happen this year."