Senna, three-times world champion, died after crashing his Williams car at the Imola race track on May 1, 1994, during the San Marino Grand Prix.
Head and Newey were acquitted of manslaughter charges after a trial in Bologna in 1997 and that verdict was upheld by an appeals court in 1999.
But Italian media reported on Tuesday that the country's highest appeals court had annulled the appeal verdict due to "material errors" and ordered the appeal be held again.
No date has yet been set for the new appeal but it is likely to be heard within a year.
At the appeal in 1999, the prosecution asked for a one-year suspended sentence, claiming Head and Newey were responsible for the crash which resulted in Senna's death.
Prosecuting magistrate Rinaldo Rosini argued at the original appeal that a poor weld on Senna's steering column had snapped as the Brazilian entered the notorious Tambarello curve at Imola.
He said this caused Senna to lose control of his car and smash into a concrete wall at 220 kph.
Rosini said that Head and Newey, as two of the most senior technical officials in the Williams team at the time, should be held responsible -- they both denied the charge.
The accusation was the same as that made at the original trial of Head, Newey and four other defendants including team chief Frank Williams, who were all acquitted in December 1997.
Lawyer Roberto Causo, who is representing Williams in the case, said he had little doubt that the original acquittal would again be upheld.
"This has an importance in terms of the formalities but in substance it changes nothing for us. We are calm -- we won in the two other (trials) and I do not see why we should fear losing in the third," he told the daily Gazzetta dello Sport.
The decision is unlikely to be welcomed by the sport however.
The fact that Italian authorities took the Senna case to court dismayed racing authorities, who warned that teams might not come to Italy if they risked conviction in the event of accidents.
Leading figures in Formula One argued that motor racing was a dangerous sport and that organisers should be exempt from any liability of serious injuries or deaths.
Four other cases over the last 40 years involving fatal crashes at Italian motor events have all ended in acquittals.