The midfielder, currently representing Germany at the World Cup, has a contract at the Allianz Arena that expires in 2015, and he has failed to agree terms on a new deal.
Madrid have long been credited with an interest in the player, with Bayern reportedly willing to sanction a £19.8 million (€25m) sale in an effort to prevent Kroos leaving on a free transfer next summer.
And though Beckenbauer says he would be disappointed to see Kroos exit the club, he understands the appeal for the player to join the European champions.
"As honorary president of Bayern I regret his departure. If he is going we will have lost a player of absolutely world class quality," said Beckenbauer to the official German Football Federation (DFB) website.
"But there is also a future in his career. This can be an experience abroad and going to a club like Real Madrid is priceless."
Kroos is among the nominees for the World Cup Golden Ball prize, awarded to the best player during the tournament.