Federal police cars are parked in front of the headquarters of Odebrecht, a large private Brazilian construction firm, in São Paulo, Brazil, June 19, 2015. Former President Luiz Inácio "Lula" da Silva may face a probe over his ties to the firm's CEO, Marcelo Odebrecht. Reuters/Rodrigo Paiva

Brazil’s investigation of the kickback and bribery scheme that already has taken down dozens of politicians may soon envelop its most high-profile figure yet. Last week’s arrest of two construction CEOs over alleged involvement in the scheme is bringing the scandal closer than ever to former President Luiz Inácio "Lula" da Silva, who already is facing scrutiny over accusations of influence-peddling with one of the construction giants.

On Friday, Brazilian authorities netted their biggest arrests so far in the scandal, known as “Operation Car Wash.” Marcelo Odebrecht, the billionaire CEO of Odebrecht SA, one of Brazil’s largest and most influential construction conglomerates, was arrested along with Otavio Azevedo, the CEO of construction firm Andrade Gutierrez, and 10 others accused of helping inflate construction contracts with the state-run energy giant Petrobras, with kickbacks paid to politicians from the ruling Workers' Party.

Neither of the magnates has been indicted, and neither Lula nor Brazil’s current president, Dilma Rousseff, has been implicated in the scandal. But Lula and Odebrecht have personal and institutional connections that are now subject to more scrutiny after last week’s arrests. In May, federal investigators opened a separate preliminary probe to examine whether Lula used his influence to help Odebrecht win contracts with foreign governments between 2011 and 2014. Prosecutors have two more months to decide whether they will open a full investigation on the former president’s ties to Odebrecht.

“There is a larger connection between Lula and Odebrecht and we see [Odebrecht’s] possible indictment as a big risk,” Cameron Combs, a Latin America researcher at Eurasia Group, told Reuters.

Although Lula is not accused of involvement in the scandal himself, any improper ties discovered between him and Odebrecht will tarnish Lula's reputation as one of Brazil’s most popular leaders, particularly as he is considered a possible contender for re-election in 2018. The Workers' Party, which he helped found, already has been severely weakened by the takedown of several party leaders in their involvement with the scandal thus far.

Folha de São Paulo, one of Brazil’s most prominent newspapers, reported Saturday that Lula told allies he was concerned he could soon be called to testify in the Petrobras investigation over his connections to the construction firms, given that he doesn’t have the same privileges as sitting politicians to avoid testifying. According to the newspaper, Lula also reportedly criticized Rousseff’s handling of the Petrobras scandal, saying her government had been "silent” in the face of the crisis.

Rousseff’s popularity has plunged dramatically in the wake of the Petrobras scandal and Brazil’s economic struggles. On Monday her approval rating stood at just 10 percent, according to Folha de São Paulo.