Kerviel, 39, was sentenced to three years in prison in 2010 after being convicted of breach of trust, forgery and entering false data.
But he insists his employers were aware of his actions.
He was given a conditional release in September 2014 after spending less than five months behind bars.
Kerviel is basing his bid on fresh evidence from Nathalie Le Roy, a top detective in the case, who testified behind closed doors in April 2015.
In a bombshell revelation in January, Le Roy said that she felt Société Générale had manipulated her during the investigation in 2008.
She presented recordings made in June 2015 of a former deputy prosecutor in the case, Chantal de Leiris, who said it was "obvious" that the bank was aware of Kerviel's dealings.
"When the subject comes up, anyone even a little bit involved in finance laughs, knowing very well that Société Générale knew," says de Leiris. "It's obvious."
The bank has rejected what it called new media manipulation in the case.
Kerviel was initially ordered to repay to Société Générale the 4.9 billion euros he lost but an appeals court overturned the order, arguing that the bank's internal oversight mechanisms had failed.
Société Générale launched a fresh court bid to recover the money in January but a decision was delayed until mid-June, awaiting the decision on whether Kerviel would face a retrial.