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The former Netherlands international joined Bayern from Real Madrid in a £20m deal in 2009 and has gone on to make 198 Bundesliga appearances.
Robben has started seven of the champions' 13 league matches this term and is now looking for a new club to join at the end of the campaign when his existing contract expires.
"It's my last year at Bayern," he is quoted as saying by Omnisport. "It has been 10 beautiful years. But it's time [to leave] now."
Fellow Bayern veteran Franck Ribery will also depart the Bavarian giants next summer.
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