Andrade Gutierrez agreed with Brazil's prosecutor-general and other investigators to pay a fine of 1 billion reais (£179 million) in leniency and plea deals covering the company and its executives, the Folha de S.Paulo newspaper said. The paper did not say how it obtained the information.
A source with knowledge of the talks said Andrade Gutierrez's Chief Executive Otávio Marques de Azevedo was negotiating a plea deal with federal prosecutors but did not say what he might reveal in exchange for a reduced sentence.
Brazil's biggest corruption investigation ever has seen some of the country's most powerful politicians and businessmen jailed over the past two years, but shed little light so far on the soaring costs of a dozen World Cup stadiums.
Federal prosecutors in the southern city of Curitiba have signed leniency deals with four companies, without disclosing their names. Brazil's comptroller general (CGU) and anti-trust regulator CADE are also negotiating leniency deals with firms.
A CGU spokesman said Andrade Gutierrez was one of seven engineering firm negotiating a deal to avoid being blacklisted from future government contracts, but that no agreement had been reached yet.
Andrade Gutierrez, which declined to comment, built the Amazonia Arena in Manaus and worked on the reform of World Cup venues in Rio de Janeiro, Porto Alegre and the capital Brasilia.
The cost of those construction projects jumped from 2.5 billion reais in early estimates to a final outlay of 3.4 billion reais, according to Contas Abertas, a group that monitors public spending.
Cost overruns and opaque decision-making in the run-up to last year's World Cup triggered an unprecedented wave of public protests in 2013, just before a team of investigators uncovered evidence of a vast price-fixing and political kickback scheme surrounding the oil company known as Petroleo Brasileiro SA.
The probe has since exposed signs of bribery on a massive hydroelectric dam and a nuclear plant run by electric utility Eletrobras, or Centrais Eletrais Brasileiras SA, and seen the jailing of dozens of executives and lawmakers.
Azevedo was arrested in June, and charged with corruption in July.
Federal prosecutors declined to comment on the report and police did not respond to requests for comment.
(Reporting by Caroline Stauffer; Additional reporting by Aluisio Alves; and Andrew Downie in Sao Paulo, Anthony Boadle in Brasilia; Editing by Brad Haynes and Bernadette Baum)
