Dassault has sent a letter to parliament -- which has yet to approve the November decision -- offering 18 Rafale planes for 2.7 billion francs ($2.96 billion), reported Le Matin Dimanche, which
said it had seen the letter.
In November, Dassault lost out on a bid to replace Switzerland's ageing F5 fighter fleet when the Federal Council opted instead to buy 22 Saab Gripen fighter planes for an estimated 3.1 billion francs.
But parliament still has to approve the decision.
"Yes, I have received this letter," Hans Hess of the parliament's security commission told the newspaper.
Hess gave no further details but said it would be discussed by the upper house group on February 13th.
Defence Minister Ueli Maurer meanwhile told the Sonntags Zeitung he was not aware of the offer.
The government considered Rafales, Gripens and Eurofighters produced by the EADS consortium.
In making its decision it argued that Gripen jets met airforce needs without compromising the budgets of other military branches.
Dassault was not immediately available for comment on Sunday.