The defence deal, one of the biggest ever, was to see the manufacture of the first 18 of the jets in France with the remainder to be produced under licence by Hindustan Aeronautics Limited (HAL), a state-run Indian aerospace behemoth.
The Indian Express newspaper, citing anonymous sources in its report, said that Dassault had refused to take responsibility for the 108 jets to be manufactured by HAL, sparking a row with New Delhi.
The French firm reportedly told Indian officials that New Delhi would have to negotiate two contracts, one with Dassault for 18 fighters and the other with HAL for the remaining 108 aircraft.
The defence ministry "completely rejected this suggestion and made it clear to Dassault that it (the French company) will be solely responsible for the sale and delivery of all 126 aircraft," the newspaper reported, citing sources.
Dassault is thought to have reservations about the ability of HAL, a firm renowned for its inefficiencies, to handle the complex manufacturing and technology transfers which are a crucial part of the deal.
The Rafale beat off stiff competition from six rivals from Russia, the US and Europe last year when India selected the French fighter to replace its ageing fleet.
Its main rival, the Eurofighter made by European group EADS, has remained in India and is still hoping to bag the deal in case Dassault is unable to conclude the negotiations successfully.
A Dassault spokeswoman said she was unable to comment immediately on the report when contacted by AFP.
The Rafale has carried out bombing missions in Afghanistan, Libya and most recently in Mali, where it is currently flying sorties targeting Islamist militants.
India's air force chief said in February that the country hopes to sign the deal with Dassault Aviation by the middle of the year.