Police commander Nathalie Le Roy, who is known for her "rigour and expertise", testified before a judge in April that the testimony of a former Société Générale employee cast new light on the inquiry, Mediapart says.
"During the various interviews and because of various documents I have handled, I had the feeling, then the certainty, that Jérôme Kerviel's higher-ups could not have been unaware of the positions he took," it quotes her as saying.
Le Roy was particularly struck by the testimony of a former employee in the operational risks department, according to Mediapart.
He reportedly claimed to have warned his bosses of Kerviel's activity in an email marked with a skull "to attract their attention".
Le Roy could find no trace of the email in his account but received no reply to a demand to see his boss Claire Dumas's exchanges with him.
Investigations in 2008 found that there had been several dozen alerts about Kerviel and that the bank had ignored them.
Le Roy also complained that Société Générale guided her towards witnesses it wanted to be heard and ignored her requests if it felt like it.
Public prosecutors "seem to have forgotten any notion of equitable justice in ureservedly supporting Société Générale's position", Mediapart comments.
The bank has always insisted that it was unaware of its trader's activity and the courts accepted that version and sentenced him to three years in prison plus two years suspended.
But an appeals court did throw out an order to pay 4.9 billion euros in damages to the bank and a new trial is to take place on January next year to establish who was responsible for the 6.3-billion-euro losses it claims to have suffered.
That's not enough for Mediapart, which wants the investigation to be reopened.
The justice ministry rejected the call on Monday.