A source for the French firm, who declined to be identified, said it was unclear how quickly the winning bid to supply the 126 jet fighters would be announced.
The source said it would reveal its bid on November 4.
"It could be settled in one day or it could take months if the (price) gap is narrow," the source said.
The Rafale and the Eurofighter Typhoon were shortlisted for the contract in April, beating fierce competition from US giants Boeing and Lockheed Martin.
Other bidders included Sweden's Saab AB and the Russian makers of the MiG 35.
The Eurofighter is made by the four-nation European Aeronautic Defence & Space consortium, representing Germany and Spain, Britain's BAE Systems and Italy's Finmeccanica.
The contract includes the outright purchase of 18 combat aircr