Lawyers representing the Stiles family say the FA, as well as the Football Association of Wales and the International Football Association Board, did not take adequate action to reduce heading the ball in training and during matches.
They also claim on-pitch assessments of players showing symptoms of concussion are "not fit for purpose".
Stiles died in October 2020 aged 78 having suffered from dementia and was found to have chronic traumatic encephalopathy, a progressive brain condition caused by repeated blows to the head.
His son, John Stiles, said: "Since dad died, I have been part of a campaign to address the ongoing scandal of dementia in football in all its various aspects.
"This potential lawsuit is part of this overall campaign for justice for the victims, like dad, and for fundamental change in an industry that continues to cause the death and illness of thousands of players (professional and amateur, men and women) every year."
The FA, FAW and IFAB have been contacted for comment.