The PFA and FIFPRO have written to football's rulemakers, the International Football Association Board (IFAB), to encourage the introduction of trials testing the use of temporary concussion substitutes.
The Premier League has been trialling permanent substitutions, allowing teams to replace any player with a head injury even if they have already used up their three substitutes, with West Ham's Issa Diop the first player to use the system.
However, the PFA and FIFPRO highlighted that the current system still requires an immediate decision be made on a player's wellbeing, when something as serious as a concussion often requires lengthy analysis.
"In England, since the trial began, we are aware of two incidents where a temporary substitution option would have better protected players," a statement read. "In each case, the players suffered from a head injury but, following an initial on-field assessment, continued to play. They were subsequently removed when it emerged their head injury was worse than first thought.
To try and take concussion protocols one step further, the two organisations called on the IFAB to introduce temporary substitutions, which would allow players to briefly leave the field for examination while a substitute takes their place.
"The reality of the in-game situation is loaded with pressure," they continued. "Medical teams can be presented with a situation where a globally broadcast match is on hold, awaiting their assessment. They have to make a potentially game-altering decision in a multi-billion-pound industry.
"We have no doubt medical teams act in the sole interests of the players. However, the rules do not do enough to support medical personnel. Pressure on them will be amplified with the return of crowds. It is also important to note that players often try to continue playing while unaware of further potential risk to their health, and the possibility of a delay in the onset of symptoms.
"Temporary concussion substitutions have been used successfully in other sports. Furthermore, a new FIFPRO poll of 96 professional football club doctors from the first-tier Belgium, English and French leagues, show that 83% believe that the use of temporary concussion substitutions would form an effective part of future protocol. (The poll is part of a research paper recently submitted to BMJ Open Sport & Exercise Medicine).
"Player safety and welfare is paramount, and should be the only priority. Therefore, we are writing to ask that IFAB’s Board of Directors extend the scope of the 18-month trial to include parallel trials for temporary concussion substitutions starting no later than the June 1, 2021."