Germany booked their place in the last eight with a comfortable 3-0 victory over Slovakia at Stade Pierre-Mauroy on Sunday.
Their opponents in the quarter-final will be the winner of the round-of-16 clash between defending champions Spain and 2012 runners-up Italy, who knocked out Joachim Low's side en route to that final.
Despite criticism of a lack of star quality in Antonio Conte's squad, Beckenbauer would prefer to face the holders in the next stage.
"Big compliments for that win against Slovakia. The quarter final will be against Spain or Italy now," he told Bild.
"Spain is more flexible, but still I'd rather have them as opponents. Italy eliminated us too often without being the better team.
"Still, no matter who it is, we don't need to be scared."
Hosts France have been tipped to challenge for a first title since Euro 2000, but Beckenbauer thought they looked "clumsy" when coming from behind to beat Republic of Ireland 2-1 in the last 16.
"They had players who ran into each other several times," the German continued.
"In a round-of-16 match at a European Championship, for a title candidate it looked clumsy."