Sepp Blatter has described penalty shootouts as a "tragedy" and is hoping an alternative solution can be found.
Both the African Nations Cup and Champions League finals this year were decided on penalties, and the World Cup final has twice - in 1994 and 2006 - gone to a shootout.
FIFA president Blatter has now called on Franz Beckenbauer, head of the Football Task Force 2014 that has been charged with recommending rule changes, to come up with another means of deciding matches.
"Football can be a tragedy when you go to penalty kicks," Blatter told the FIFA Congress in Budapest. "Football should not go to one to one. When it goes to penalty kicks, football loses its essence.
"Perhaps Franz Beckenbauer with his football 2014 group can show us a solution - perhaps not today but in the future."
Beckenbauer, an honorary president at Bayern Munich, had said Chelsea were deserving Champions League winners in the wake of their shootout victory over his former club at the Allianz Arena.
"Why are the English to blame when Bayern are not able to convert their dominance? Luck was on Chelsea's side this time and that is why they are deserved Champions League winners," he had said. "Nonetheless, Bayern was the better team for most parts of the game."
FIFA had come up with the 'Golden Goal' concept in 1993 in which sudden death would apply during extra-time, while the watered-down 'Silver Goal' concept was later introduced. Both ideas were abandoned after Euro 2004 as they were seen to encourage negative football.