Beckenbauer urges centre-circle handshakes
"You could convene in at the halfway line and then go off the pitch together," the former West Germany captain and coach said on Wednesday. "That's what we used to do when I was at school."
Beckenbauer, heading a task force which is looking at ways to make the 2014 World Cup more entertaining than the previous tournament, said that fair play was one of his group's priorities.
"We've seen so many images of players behaving badly. Fair play is important because players and coaches are role models and should behave like role medals," he said.
Beckenbauer said another idea discussed by his group was that players should emerge together for the second half.
"These are small things which could improve the image of football," he said.
Pre-match handshakes have become a big issue in England after Uruguay's Luis Suarez snubbed Patrice Evra before a Manchester United-Liverpool game earlier this month.
Suarez had just served an eight-match ban after being found guilty of racially insulting Evra in a previous game.
Beckenbauer said the players often missed shaking hands at the end of a game "because they go off to celebrate with their fans or they want to celebrate with their grandmother."