Amid growing pressure and uncertainty, the Games were pushed back until 2021 due to the coronavirus pandemic.
It majorly impacts men's soccer, with teams usually made up of under-23 players, but several athletes are likely to be affected by the postponement.
FFA CEO Johnson said he wanted consideration from FIFA for that to be changed for the Tokyo Olympics.
"Men's football at the Olympics is an under-23 tournament but we would like to open up discussion with FIFA and the Asian Football Confederation [AFC] to consider adjusting the men's soccer tournament so that it becomes an under-24 tournament for the Tokyo Olympic Games," he said in a statement on Thursday.
"This would ensure the players who helped their nation qualify for the Games this year but might otherwise be ineligible for the tournament next year because of age restrictions, have an opportunity to fulfill their dreams of representing their country and becoming Olympians."
Australia's women's team also qualified for the Olympics, which will be held no later than the northern summer of 2021.
Johnson backed the decision to postpone the Games, saying: "Our football community are rightly proud of the efforts and achievements of the Matildas and the under-23 men's national football team to qualify for Tokyo.
"We must, however, ensure the health and wellbeing of the athletes, officials, volunteers, and fans is prioritized. We are glad that the IOC, AOC and all parties involved have reached this decision.
"When the dates of the potentially rescheduled Tokyo 2020 Olympic Games are known, FFA will work with its national teams unit and the AOC to plan the best possible preparations for both sides."