France and French manufacturer Dassault Aviation have been trying for years to sell the jets abroad without success. The Rafale has been in service for the French Air Force since 2006.
Defense spokesman Sitanshu Kar said Tuesday that Indian Defense Minister Manohar Parrikar met with his French counterpart, Jean-Yves Le Drian, on Monday as part of an official visit to India.
"All issues related to defense were discussed, including the Rafale," Kar said. "Both sides decided to adopt a fast-track approach wherever there are differences."
A French defense official, who was not authorized to discuss the matter publicly, also said that the two defense ministers agreed to accelerate negotiations.
"We can say this morning that the negotiations are on the cusp of conclusion," the French official said.
French President Francois Hollande, speaking briefly to reporters outside Paris, said "good progress" has been made, but that "it's necessary to be prudent on such contracts. When it's finalized, we can speak about it. Until now, silence has rather been the right method."
India has become the world's biggest arms importer, with an economic boom enabling it to modernize its military. Major arms manufacturers are wooing the country as it replaces its obsolete Soviet-era weapons and buys new equipment. India already has a fleet of the older Mirage jets, France's last big-name fighters.
India's air force has around 700 fighter aircraft and is exceeded in size only by the United States, Russia and China.
Growing worries about China's fast-expanding military and the decades-old mistrust of Pakistan have fueled India's impetus to add heft to its defense forces.
The Rafale has struggled to find an export market because of its high cost, complexity and a design that was a marked shift from the Mirage.
Competing jets from the United States and Russia, such as the General Dynamics F-16, McDonnell Douglas F-15 and Sukhoi Su-27, have grabbed a large slice of the market.
Deals for Brazil, Libya and Switzerland to buy the Rafale have all fallen through, often at the last minute.
In 2007, Morocco opted for F-16s instead of Rafales, with French media blaming bungled negotiations by the French government involving the lack of a single dedicated coordinator to handle talks with Rabat.
France has used Rafales in several combat missions in recent years: over Libya in 2011, in Mali last year and currently as part of the international campaign against Islamic State militants in Iraq from a French air base in the United Arab Emirates.