Massa subsequently crashed head on into a tyre barrier at a speed of about 190 kilometres per hour. He underwent emergency surgery on Sunday after being rushed by helicopter from the Hungaroring to hospital.
The Ferrari driver may also be moved from Budapest to the Paris clinic of Gerard Saillant, who treated Brazilian football star Ronaldo and former Formula One driver Michael Schumacher in the past.
Luis Antonio Massa said if his son's recovery proceeded at the same speed he could be moved out of intensive care in two days.