Shortly after his swearing in as the head of state, Zardari told a news conference that he would attend the UNGA, where he would take up Pakistan's request to probe the assassination of his wife, former premier Benazir Bhutto, as a "victim of terrorism".
Diplomatic sources were quoted by The News as saying that there was a 'definite desire on both sides(Pakistan and India) that the two leaders" should meet on the sidelines of the UN meet'.
In his first utterances after assuming office, Zardari vowed to work with all of Pakistan's neighbours to solve regional problems and said there would be "some good news" about efforts to resolve the Kashmir issue within this month.
The sources indicated that date and time for such a meeting would be worked out through diplomatic channels.
Reports have suggested that the meeting between Singh and Zardari is expected to take place between September 24 and 26.
The head of the Pakistani delegation is scheduled to address the world body on September 25 while the Indian team's leader will make his address the following day.
Earlier, there were indications that Prime Minister Yousuf Raza Gilani would lead the Pakistani delegation to the UNGA, but this has changed after Zardari's elevation as President.
A possible meeting between Singh and Zardari would be the second high-level political contact between the two countries since last month's meeting between the prime ministers of India and Pakistan on the sidelines of the SAARC summit in Sri Lanka.
Ties between the two countries were strained by the suicide bombing on the Indian embassy in Kabul, with both Indian and Afghan officials saying that Pakistan's Inter-Services Intelligence agency was linked to the attack.
The protests in Jammu and Kashmir also affected ties, with India slamming comments on the matter by Pakistani leaders as interference in its internal affairs.
Matters were exacerbated after Pakistan's parliament decided to set up a committee to monitor the situation in Jammu and Kashmir and take up alleged rights abuses in the Indian state. The composite dialogue process too was affected by these developments.
However, after Zardari's assumption of office, both countries have indicated a desire to work together.
In his congratulatory message to Zardari, Singh said the ushering in of democracy in Pakistan offered new opportunities to transform bilateral ties.
"We have the political will to work with you to seize these opportunities and transform our relations. In your new office, you will find a friend in India," Singh said.
At his first news conference after assuming office, Zardari said the Pakistan government intended to take his country "and our neighbours into the 21st century together".
He added: "We shall stand with each other, we shall not stand in each other's way. This is a message not just for Afghanistan but for all the neighbouring countries in our region."
More from rediff