Massa believes he was the victim of a conspiracy to cover up the 2008 Singapore GP Crashgate scandal in which Renault's Nelson Piquet Jr crashed on purpose to let team-mate Fernando Alonso win.
If the race result had been thrown out at the time, Massa would have claimed the drivers' championship instead of losing it to McLaren's Lewis Hamilton by one point.
Massa has assembled a comprehensive legal team that alleged the Brazilian suffered "tens of millions of euros" of missed income as well as reputational harm and had set a 12 October deadline for the FIA and FOM to respond to its queries or face it in the UK's High Court.
His legal team has now said it has granted both bodies until 15 November to finish their investigations before taking next steps.
"FIA and FOM are completing an internal investigation and have requested one last extension to the deadline they initially asked for, from 12 October to 15 November," said Massa's lawyer Bernardo Viana.
"We have agreed to this final period because if the new administration is indeed looking into the matter in good faith, they will certainly reach the same conclusion we and so many people around the world have.
"We would like to know what Formula 1's new leadership's position is on the recently disclosed scandal and the injustice faced by Felipe Massa."
Speaking to Autosport sister site motorsport.uol.com.br at last weekend's Stock Car Series round in Buenos Aires, Massa said he still hopes Ferrari - his team at the time - will lend him support in the matter.
"To be honest, we spoke in the letters on the legal side, but I don't see the point why Ferrari would not be on my side," he said.
"Because we lost the championship, they took away the championship from us, from me and from Ferrari. When you hear Toto Wolff speaking about 2021, Ferrari needs to do the same.
"Ferrari needs to fight for the best of the team and I don't see really Ferrari away from the manipulation which happened to me.
"For the moment, they didn't really say, 'Okay, we are together'. I think they are waiting to see what's going to happen."
Speaking at last month's Singapore Grand Prix, Mercedes chief Wolff said he would follow the matter "with interest" given the team's grievances over the conclusion of the 2021 championship in Abu Dhabi, but added that he doesn't believe Massa's challenge will be successful.
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"I don't think he has a case, to be honest," said Wolff. "We are signing up to sporting regulations. They're very clear, and you commit as a licence holder.
"If everybody were to open up situations then the sport would be in disarray."
Additional reporting by Federico Faturos
