Permanent concussion substitutes are currently being trialled, but there are demands for more to be done to protect player welfare.
FIFPRO and the PFA want temporary concussion substitutions and have written a joint letter to IFAB explaining their reasoning.
They are concerned that permanent substitutions do not give medical teams the appropriate environment to assess a player with a potentially serious head injury.
In a letter, the unions wrote: “Since the beginning of IFAB’s permanent concussion substitute trial, we have seen several incidents where the new laws of the game have fallen short of their objective and jeopardised player health and safety.
“We write to ask for the existing trial to be extended in order to test in parallel temporary concussion substitutions as soon as possible.
“In England, since the trial began, we are aware of two incidents where a temporary substitution option would have better protected players.
“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.
“Both of these incidents were in the Premier League, where the trial is taking place, and concerned West Ham United’s Issa Diop and Sheffield United’s George Baldock.
“These cases underline our concern that permanent substitutions do not give medical teams the appropriate environment to assess a player with a potentially serious head injury.
“The reality of the in-game situation is loaded with pressure. 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.”