Global and English players' unions have written to football's lawmakers calling for temporary concussion substitutes to be included in current trials as "player health and safety had been jeopardised" this season.
Permanent concussion substitutes were introduced to English football at the turn of the year, allowing additional changes for head injuries.
But world union FifPro and the Professional Footballers' Association say temporary substitutions would have "better protected players".
They cite incidents with West Ham's Issa Diop and Sheffield United's George Baldock as examples to back up their stance.
Temporary substitutes, already used in rugby union, allow for a player to be replaced while a head injury assessment is carried out on a player.
In both cases cited, Diop and Baldock were allowed to continue playing following a head injury, before then being substituted.
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In the letter written to lawmakers IFAB, the unions say that the use of temporary substitutes should be added to football's ongoing 18-month trial and should start "not later that 1 June 2021".
They also say a recent FifPro poll of 96 professional football club doctors from the first tier of the English, French and Belgian leagues shows that 83% believe the use of temporary concussion substitutes "would inform an effective part of future protocol".
"These [Diop and Baldock] cases underline our concern that permanent substitutes do not give medical teams the appropriate environment to assess a player with a potentially serious head injury," the letter added.
The stance from both unions echoes that of head injury charity Headway, brain injury expert Dr Willie Stewart, and campaigners Dawn Astle and Chris Sutton, both of whose fathers had brain injuries linked to playing football before they died.
The Football Association and IFAB have explained that the decision to hold a trial with permanent substitutes this season is on the advice of medical experts at Fifa, who say it is a safe measure.
The FifPro and PFA letter adds: "The reality of the in-game situation is loaded with pressure.
"We have no doubt medical teams act in the sole interests of players. However, the rules do not do enough to support medical personnel. Pressure will be amplified on them with the return of crowds.
"Player safety and welfare is paramount and should be the only priority."