If confirmed, the revelations in a 400-page statement seen by weekly news magazine IstoE provide ammunition to Rousseff's opponents, who are trying to impeach her or invalidate her 2014 re-election.
Amaral was the leader of the Workers' Party in the Senate and Rousseff's point man on economic policy until his arrest in November on obstruction of justice charges. He was released from jail on Feb. 19, just days after his plea statements to prosecutors, IstoE reported.
Amaral reportedly testified that Rousseff had used her influence to keep directors suspected of corruption in positions at Petrobras.
The state-run oil company formally known as Petroleo Brasileiro SA is at the centre of the massive bribery and political kickback scandal.
IstoE said Amaral testified that Rousseff tried on three occasions to use the Justice Ministry to interfere in the Petrobras graft investigation and get suspects released from prison.
Amaral reportedly detailed illegal funding of Rousseff's 2010 election campaign and said she knew all about the purchase of a refinery in Pasadena, Texas, that cost Petrobras many times more than it was worth.
Reports of Amaral's plea bargain shocked the Rousseff government, which scrambled to contain the damage by questioning the credibility of a politician who is being prosecuted and facing expulsion from the party and the loss of his Senate seat.
Rousseff met with her key political advisors at the presidential palace on how to deal with Amaral's reported allegations, two of her aides said. Her office said it had no comment for now.
"Senator Amaral has not excelled at telling the truth," said Jose Eduardo Cardozo, who was Rousseff's justice minister until Thursday, when he became her government's solicitor general.
"Regrettably, he has no credibility to make any accusations."
The online version of Brazilian paper O Estado de S.Paulo said the statements by Amaral were preliminary testimony outlining what he could reveal if granted leniency in a formal plea bargain.
The public prosecutor's office said it could not comment on plea bargains until the Supreme Court approves them as valid evidence.
Amaral's lawyer had previously said that his client would not make a plea bargain. Attempts to reach his offices for comment on Thursday were unsuccessful.
IstoE said Amaral had accused Rousseff of appointing a favourable Supreme Court justice to help avert conviction of some directors and statesmen under investigation for bribes and kickbacks at Petrobras.
Amaral also said Lula had full knowledge of the bribery and political kickback scheme, which siphoned billions of dollars off overpriced contracts with Petrobras, and tried to block prosecutors from investigating it, according to IstoE.
Executives of the country's top engineering firms have been jailed on charges of corruption and price-fixing. Dozens of politicians in Rousseff's governing coalition are under investigation for receiving bribes.
Lula's foundation declined to comment on the reports. "We do not know if this plea bargain even exists," Lula Institute spokesman José Chrispiniano said. "(IstoE) has exaggerated in the past."
Lula, who founded the Workers' Party and was president from 2003 until 2010, is under investigation by federal prosecutors who suspect he received undue favours while in office from engineering firms they are probing.
His standing as Brazil's most popular politician has been hurt by another probe that involves a beach-front penthouse and country estate that were allegedly renovated for him by OAS and Odebrecht, two of the biggest builders implicated in the Petrobras scandal. He denies ownership of the properties.
Prosecutors presented formal charges against Amaral on Dec. 7, along with billionaire financier Andre Esteves, accusing them of obstructing a criminal investigation related to the Petrobras graft scheme.
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