(Adds background)

BRASILIA, May 3 (Reuters) - Brazil's top prosecutor requested that President Dilma Rousseff be investigated for trying to obstruct a sweeping corruption investigation involving state-run oil firm Petrobras, local media reported late on Tuesday.

An investigation could well mark the political end for the beleaguered leader of the world's seventh-largest economy as it would be the first time that Rousseff would be directly implicated in Brazil's biggest-ever graft case.

She is already likely to be suspended from office as early as next week on unrelated charges of breaking budgetary laws.

The corruption scandal casts a shadow over 13 years of Workers Party rule that saw Brazil's middle class expand by some 40 million people since 2003 with the help of new social programs.

Rousseff has consistently maintained she has done no wrongdoing, despite serving as the chairwoman of Petrobras' board for several years when much of a billion-dollar kickback scheme played out.

The case has already seen executives from Brazil's biggest construction firms jailed and convicted for siphoning funds from Petrobras to bribe politicians. Around 50 politicians are under investigation, including the leaders of both houses of congress.

Neither Brazil's Supreme Court, which must authorize any investigation into Rousseff, nor the office of Prosecutor-General Rodrigo Janot returned calls and emails requesting confirmation of the request for investigation.

Globo News, Brazil's largest media conglomerate, along with the Estado de S.Paulo and Folha de S.Paulo newspapers reported the request made by the prosecutor at close to midnight on Tuesday.

The request will be analyzed by Supreme Court justice Teori Zavascki and is not public because it is based on recorded phone calls between Rousseff and former President Luiz Inacio Lula da Silva, news site G1 reported.

Federal Judge Sergio Moro in March made public taped phone conversations between Rousseff and Lula that fed opposition claims that Rousseff had tried to name Lula as her chief of staff in order to shield him from prosecution.

LULA CHARGED

Newspaper Estado de S. Paulo also reported on Tuesday that Janot had charged Lula with participating in a scheme to stop former Petrobras executive Nestor Cervero from collaborating with the investigation. The federal prosecutors' office would not confirm the charge.

The Supreme Court did confirm that Janot had asked for Lula and several of Rousseff's ministers to be formally investigated, including Chief of Staff Jaques Wagner, the minister in charge of legislative affairs, Ricardo Berzoini, and Rousseff's spokesman, Edinho Silva.