Fifa are trying to persuade Zinedine Zidane and Marco Materazzi to bury the hatchet on a goodwill mission to 2010 World Cup hosts South Africa.
The pair clashed infamously during the World Cup final when Zidane was sent off for head-butting the Italian defender, who had insulted the France captain's sister.
FIFA president Sepp Blatter told a news conference in Berlin: "We are working on bringing together Zidane and Materazzi, perhaps that they should go together to Robben Island where Nelson Mandela was held in prison for 27 years.
"We are definitely working on it and that would bring an end to the story."
Blatter admitted the incident had tarnished the memory of a World Cup that had otherwise captured the imagination of millions across the globe.
Italy went on to win the final on penalties after the match ended 1-1 after extra time, and the FIFA president said he wished there had been another way to decide the victors.
He added: "It's a pity that the World Cup ended with a red card, it should never end like that.
"A World Cup final should also not be decided by penalty kicks because football is a team sport and that comes down to one on one, but we have no other solution."
