Indian Prime Minister Narendra Modi said in April he had ordered 36 Rafale fighters to modernise his country's warplane fleet, though detailed terms and conditions remained to be settled.
Modi had opted to deal directly with the French government after three years of inconclusive negotiations with the plane's manufacturer, Dassault.
"Things are getting better with India," the source said. "An agreement could be seen in about 10 days."
Dassault Aviation was not immediately available to comment.
India's announcement came after Dassault in February won its first export order for the jets from Egypt. Since then, Qatar has also placed an order, and talks are under way with Malaysia and the United Arab Emirates.
But the Indian deal ran into trouble, with both sides wrangling over the unit price of the aircraft and a condition that Dassault should invest a big percentage of the value of the multi-billion dollar contract in India, sources said earlier this month.
India is keen to modernise its ageing airforce, with military officials having warned of a major capability gap opening up with China and Pakistan without new Western warplanes, or if local defence contractors cannot build what the military needs in a timely manner.