A new order in which kicks are taken, described as ABBA, could be trialled this year under proposals discussed by the International Football Association Board (IFAB) during its Annual Meeting at Wembley on Friday.
Currently penalty shootouts see team A and team B take five penalties each in an alternating pattern with sudden death used after that if the scores are level.
IFAB says research proves the team taking the first penalty has a 60 percent chance of winning.
They are keen to try a new sequence which replicates the switch of serve between tennis players in a tiebreak.
It would involve team A taking the first penalty, team B the second and third, team A the fourth and fifth and so on until each team had taken five.
Stewart Regan, IFAB board member and Scottish FA chief executive welcomed the proposal, one of several discussed.
"The stats at the moment say 60 percent of penalty shootouts are won by the team that takes the first kick," he told reporters. "We believe that the ABBA approach could remove that statistical bias and it's something we would look to trial."
IFAB, made up of the four British FAs and world governing body FIFA, also confirmed on Friday it had scrapped the law which saw an automatic yellow card for a player giving away a penalty, provided a genuine attempt was made to play the ball.