The three countries have discussed the pipeline for years. They have agreed in principle on a pricing formula but India dropped out of talks in mid-2007, saying it first wanted to resolve issues with Pakistan such as transit fees.
India and Pakistan said on Friday they were just days or weeks away from finalising terms on the cross-border pipeline. Iran and Pakistan had previously said they would go ahead with the project without India if necessary.
"It looks like arriving at this agreement will not be out of reach," Iranian Foreign Ministry spokesman Mohammad Ali Hosseini told a news conference.
"And it is natural that the matter — one of the most important issues of interest by the three parties — will be discussed in the trip by the president," Hosseini said. "We are hoping the project … will be finalised soon."
Ahmadinejad is due to visit Pakistan on Monday, where he is expected to meet his Pakistani counterpart Pervez Musharraf, and India on Tuesday. The Iranian president is to make the stopovers while travelling for an official visit to Sri Lanka.
The $7.6 billion project has been dubbed the "Pipeline for Peace and Progress" because of the mutual benefits it will bring to India and Pakistan, two countries that have fought three wars since they were divided by the partition of India in 1947.
The nuclear-armed rivals are both desperate to tie up future energy supplies to fuel their fast growing economies.
The United States has tried to discourage India and Pakistan from any deal with Iran in the past because of Tehran's suspected ambitions to build nuclear arms. Iran denies any such ambitions.
The pipeline would initially transport 60 million cubic metres of gas (2.2 billion cubic feet) daily to Pakistan and India, half for each country. The pipeline's capacity would later rise to 150 million cubic metres.
Iran has the world's second largest reserves of gas after Russia but has been slow to develop exports partly because of U.S. sanctions.
