Nicknamed "Der Bomber" for his scoring prowess, Mueller, a 1974 World Cup and 1972 European Championship winner, who also won three consecutive European Cups with Bayern, has been suffering from the disease since early this year.
"For some time now Gerd Mueller has unfortunately been ill," Bayern said in a statement ahead of Mueller's 70th birthday next month.
"He is suffering from Alzheimers. Since February 2015 Gerd Mueller has been treated professionally with strong support from his family."
Mueller, who won 13 titles at Bayern, played for the club from 1964 to 1979, scoring 533 goals in 585 games in all competitions -- 365 in the Bundesliga.
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He also scored 68 goals in 62 appearances for Germany, a mark surpassed only recently by Miroslav Klose.
Mueller also played for two years at the Fort Lauderdale Strikers in the United States before returning to Bayern to work as a youth coach.
"Bayern will always support Gerd Mueller and his family, whenever necessary," said club CEO Karl-Heinz Rummenigge.
"Gerd Mueller is one of the greats of world football. Without his goals Bayern and German football would not be what they are today. Gerd was the kind of striker you will most likely never see again."
His turn and speed plus his ability to score from every position made him the iconic figure of the 1970s Bayern and Germany teams but he was always more shy and reserved than his team mates Franz Beckenbauer and Uli Hoeness.
"We ask in this difficult situation for him and his family for the necessary respect," said Rummenigge.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
