The issue was brought to the fore on Sunday, when Arsenal defender David Luiz continued to play, despite blood seeping through his bandage after a collision with Wolves forward Raul Jimenez, who was left with a fractured skull.
It led to brain injury association charity Headway condemning present measures in place in football, and both Ederson and Klopp have supported potential change in the game.
"It was an accidental clash, head to head, very difficult. I think all the concern and care is very important. It is a part of the body that is very fragile and needs special attention.
"I agree when there is a blow to the head there should be a substitution, whether the player can continue or not. You might be feeling OK because you are warmed up, but after the game you feel the consequences.
"It was accidental. It is something that happens in games and we can't change that. They just went to compete for the ball.
"But we know the risks of a head injury. I hope he recovers quickly and will be back as soon as possible."
Klopp, meanwhile, admitted that in some circumstances, present legislation does not go far enough.
"I know we have concussion protocols and I'm pretty sure Arsenal did that. I'm not sure any rule would help in that moment because the player can play on,” the former Borussia Dortmund boss said.
"But, yes, it makes sense that we can do things like this, of course."
A concussion substitution would allow clubs the opportunity to make a ‘free’ temporary change when a player suffers a head knock, giving them ample time to assess players and to withdraw them from the game if necessary.