Police say there is no proof Mr Lula was involved but want to determine if he obtained advantages for himself or his party under the scheme.
Mr Lula has said he is yet to receive any requests from police.
Prosecutors allege firms paid corrupt officials to secure lucrative contracts with the state-owned oil giant.
The scandal is the largest in Brazil’s history, with top politicians accused of taking bribes.
Among those arrested in connection are Mr Lula’s former chief of staff Joss Dirceu and the Workers’ Party treasurer Joao Vaccari.
But Mr Lula’s successor as Brazilian leader, Dilma Rousseff, who chaired Petrobras when much of the corruption is believed to have taken place, has been cleared of involvement.
The request to question Mr Lula was first reported by the weekly newsmagazine Epoca. The court is yet to respond.
If the request is approved by the courts, former President Luiz Inacio Lula da Silva will have to go down to a police station to give his version of facts.
He is a towering love-him-or-hate-him figure in Brazilian politics.
His opponents say he is in many ways responsible for the country’s current recession and for some of the corruption scandals that have emerged in the past years.
But his supporters believe he is the only politician from the Workers’ Party who stands any chance to keep the left in power in Latin America’s largest country, and that this is why he is being drawn into the investigations.