Football's global players' union FIFPro is backing the idea of allowing a fourth substitute in games.
The International Football Association Board, the sport's rule-making body, has twice rejected proposals to allow an additional substitute in extra time of knockout matches.
But it has requested that more research be carried out on the idea.
In a FIFPro poll of players across all continents, 84% supported the idea of a fourth substitute in some form.
"The response to our survey is overwhelming," said FIFPro general-secretary Theo van Seggelen.
"Whether only applied to extra time or during the regulation 90 minutes, professional footballers worldwide surveyed by FIFPro see a need to add a fourth substitute.
"It's a position that will challenge traditional views, but the players have one of the most important roles in this debate."
Fifpro selected a representative sample of players from 27 countries and gave them the choice of three answers.
Out of 244 responses, 39 players (16%) said they were totally against a fourth substitution.
Of the remainder, 119 players (49%) were in favour of a fourth substitute but said the additional change should only be allowed in extra time. A total of 86 players (35%) were in favour of a fourth substitution even in matches of 90 minutes.
"Our research is representative of players on all continents and they have clearly shown a preference for the game to evolve and show greater flexibility, especially during matches that go to extra time," said Van Seggelen.