As the game entered a shootout, Renato Sanches hit the crossbar before Cech's replacement, Emiliano Martinez, continued the hero act with saves from David Alaba and Juan Bernat.
Muller, under contract until 2021, started Bayern's 9-1 thumping of minnows Erlangen-Bruck last weekend and subsequently travelled with the rest of the squad to the Far East for International Champions Cup fixtures against Arsenal, AC Milan, Chelsea and Inter Milan.
Robert Lewandowski scored the opening goal of the game after just eight minutes, dispatching a penalty kick easily after Ainsley Maitland-Niles fouled Juan Bernat in the box.
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It may only have been a friendly match and Arsenal emerged victorious, but it made for painful viewing at times for manager Arsene Wenger, whose side suffered a 10-2 aggregate drubbing by Bayern in last season's Champions League.
Arsenal beat Bayern Munich on penalties in Shanghai - catch up on the action. They set a club record by signing Lacazetteand were also able to secure Sead Kolasinac to strengthen their left side.
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Muller is still contracted to Bayern until 2021 and is said to "fit perfectly" with the German club's system and style of play, however, he did have a poor 2016/17 campaign and this, coupled with Rodriguez' arrival, could open the door if the price is right. Either they sell now for £50 million (S$89.2 million) or they get nothing for him next summer.
The last time both European giants faced each other was the 2nd leg of the Champions league round of 16 where Arsenal lost 5-1 in February 2017.
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