"There is an option for procurement of an additional 63 aircrafts subsequently for which a separate contract would need to be signed," a source said.
"Presently the contract under negotiation is for 126 aircraft but we are talking about the follow-up."
The Indian press has estimated the value of the deal for 126 Rafales at $12 billion (nine billion euros).
A 50% increase in the number of planes ordered would take it to around $18 billion giving a huge boost for the French defence industry.
India selected French manufacturer Dassault Aviation as its preferred candidate to equip its air force with new fighter jets in January 2012.
Under the deal on the table, the first 18 Rafales would be built in France but the next 108 would be assembled in India by Hindustan Aeronautics Ltd.
"The first aircraft will be delivered three years after signature of the contract," the source added.