The deal is just the first of a rash of tenders Rousseff is expected to oversee in her term as Brazil plans to spend billions on imported weapons in the next years to increase its military might.
"We are going to talk over the issue of the fighters -- me, Rousseff and [Defense Minister Nelson] Jobim," Lula told reporters at a news conference with Rousseff in Brasilia.
Brazil has delayed picking the winner of an international fighter jet tender for months.
The foreign aerospace giants competing for the sale to Brazil of 36 combat aircraft are France's Dassault with its Rafale fighter, Sweden's Saab with the Gripen NG aircraft and U.S. company Boeing with the F/A-18 Super Hornet.
Experts have suggested that the initial tender for 36 planes could be increased to more than 120.
The deal is estimated to be worth $4 billion-$7 billion, depending on details of the order to be agreed, defense experts have said.
Lula had suggested that he would pick the French bid before leaving office but the decision was deferred to after the election. The pick has been on hold since March, Lula told reporters.
Rousseff, Lula's former Cabinet chief, easily won an Oct. 31 runoff and will take over as head of state Jan. 1.
Both are scheduled to attend a Group of 20 summit in South Korea next week with both French President Nicolas Sarkozy and U.S. President Barack Obama also expected to attend.
The fighter jets that are due to be ordered are intended to renew Brazil's aging fleet of combat aircraft. It has long been suggested that France's Rafale fighter stands as the preferred pick of the Latin American country.
What makes the French bid attractive, experts say, is France's sweetener of transferring technology related to the supersonic Rafale so that Brazil, bent on becoming the lead military power in South America, could assemble most of the jets itself and sell them regionally.
Brazil has already signed a deal with the French for the construction of five submarines in Brazil. The deal includes building a nuclear-powered vessel.
In recent weeks Brazil also signed defense cooperation agreements with Britain, adding to a pile of similar deals with other European countries and the United States.
The signing with Britain has paved the way for the potential purchase of 11 British warships to replace the country's aging navy fleet.
Notable deaths of 2014 [PHOTOS]
Iraq seeks thousands of tank rounds