Blatter told the FIFA Congress on Friday that soccer "loses its essence" when matches are settled by penalty kicks.
Soccer "can be a drama, even a tragedy, when we go to penalty kicks," Blatter said. "Football should not go to one to one, because when football goes to penalty kicks, it loses its essence as a team sport."
Last Saturday, Chelsea beat Bayern Munich in a shootout to win the Champions League after the German side had dominated a game that finished in a 1-1 draw after extra time.
Beckenbauer, the former Bayern captain and president, heads FIFA's Task Force Football 2014 panel that Blatter created in 2010 to improve soccer before the next World Cup in Brazil.
"Perhaps Franz Beckenbauer with his Football 2014 group can present us with a solution, if not today then tomorrow," Blatter said.
The FIFA chief later clarified his view on Twitter, writing that did not want to scrap shootouts but believed that matches should be decided "11 v 11."
The task force has met several teams, but has shown little public interest in scrapping penalty shootouts.
Beckenbauer's task force deputy chairman Kalusha Bwalya also has recent experience of a shootout.
Bwalya, a Zambian playing great, saw his home nation win the Africa Cup of Nations in February on a shootout after drawing 0-0 with Ivory Coast.