Federal prosecutors who uncovered a huge corruption scheme at oil company Petrobras are looking into whether Brazil's former president Luiz Inacio Lula da Silva received undue favours from engineering firms they are investigating.

In a letter to the Supreme Court made public on Monday, the head of the investigation, Deltan Dallagnol, argued for a federal probe because some of the alleged gifts were made while Lula was still in office.

The prosecutors suspect favours were extended to Lula by executives of engineering firms Odebrecht and OAS that have been charged with corruption and money laundering in the massive bribery and political kickback scandal involving contracts with state-run Petroleo Brasileiro SA.

If the Supreme Court authorizes the probe, it would be the first time federal prosecutors will be looking to link the once wildly popular leftist president and Brazil's biggest ever corruption case.

Lula, who was president from 2003-2010, has already faced police questioning over the financial dealings of one of his sons and now faces questioning by Sao Paulo state prosecutors over his alleged ownership of a beach-front penthouse triplex and country estate.

The triplex and country home were allegedly renovated by OAS and Odebrecht. Lula has said the properties don't belong to him.

His lawyers appealed to the Supreme Court last week against the federal investigation, arguing that Dallagnol and his team had overstepped their jurisdiction by duplicating the inquiry by Sao Paulo state prosecutors.

Brazil has been rocked by the growing Petrobras scandal that has ensnared dozens of members of its business and political establishment and could now implicate Lula.

To avoid being summoned to a police station to answer questions on the properties, Lula and his wife have offered to make statements in writing, their lawyers said.

Brazil's justice minister Jose Eduardo Cardozo quit on Monday under pressure from the ruling Workers' Party over his failure to curb the corruption probe that has spread to its founding leader Lula.

His resignation weakened President Dilma Rousseff as she struggles to survive opposition attempts to impeach her or annul her 2014 reelection alleging bribe money helped funded her campaign.