The Bayern supremo highlighted the significance of the Welshman's move to the Spanish capital and believes the Liga giants are now among the favourites to win the Champions League
Players such as Gonzalo Higuain, Mesut Ozil, Raul Albiol and Jose Callejon all left Madrid this summer, meaning the club recuperated well over €100 million of the €181.5m [£153.5m] they spent this summer.
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"One thing's clear and that's that the transfer of Bale is a new milestone in football," Rummenigge was quoted as saying by TZ.
"We should not forget one thing, though, and that's that Madrid have also sold five or six players for a lot of money. That's why Financial Fair Play will not be a problem for them in this case.
"As far as I know, they made over €70 million [£60m] on the players they sold to Napoli. Plus there's the €50 million [£42m] for Ozil."
Rummenigge then went on to say that Madrid are one of the favourites to win the Champions League following the signing of players such as Bale, Isco and Asier Illarramendi.
He added: "You have to include them in a small list of favourites. My colleague [Madrid president] Florentino Perez wants to win the 10th European Cup at all costs. The people at Madrid are not very patient."