Bayern lost to Real Madrid in the Champions League quarterfinals last week and crashed out of the DFB Pokal to Borussia Dortmund in the semifinals.
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The Spain international, 26, is in his fourth year at the club and his existing deal had been due to expire in the summer of 2019.
Dortmund's German Cup semifinal win over Bayern involved character and a lot of luck. It also gave a true sense of the Bavarians' flaws.
Bayern Munich have announced they have triggered an option to sign Kingsley Coman from Juventus permanently.
Bayern Munich's treble hopes have disappeared in eight days as they once again look brittle towards the business end of the season.
Robert Lewandowski and Arjen Robben were prime culprits as Bayern Munich relinquished a 2-1 lead in a stunning semifinal defeat to Borussia Dortmund.
The Bavarians' captain was guilty of a giveaway ahead of Ousmane Dembele's winner for Dortmund in his team's 3-2 DFB Pokal loss.
Borussia Dortmund rallied to beat Bayern Munich 3-2 in their DFB Pokal semifinal at the Allianz Arena on Wednesday night.
Arsene Wenger has defended Alexis Sanchez for his late antics in Wednesday's 1-0 win over Leicester, blaming a controversial incident on the referee.
Maik Barthel said Lewandowski was "on the receiving end of harsh treatment like no other player in the Bundesliga."
Dortmund boss Thomas Tuchel said his side "have the momentum on our side" as they seek to overcome Bayern Munich in the DFB Pokal semifinals.
Bayern Munich boss Carlo Ancelotti is trying every day to convince Philipp Lahm to carry on playing but has had no luck so far.
Bayern struggled to move on from Madrid, stumbling to a 2-2 draw against Mainz at the weekend. Dortmund in the cup can prove salvation.
As Alexis Sanchez continues to stall over a new Arsenal deal, Bayern have entered the race for his signature. As always, Transfer Talk has the latest.
Bayern took the pitch three days after the controversial extra-time defeat to Real Madrid and turned in one of their worst performances of the season.
Bayern Munich captain Philipp Lahm has said now is not the time to be "sentimental" but wants to crown his playing career with a seventh DFB Pokal.
Lacklustre Bayern Munich dropped points for a third time in four Bundesliga games, stuttering to a 2-2 draw against relegation-threatened Mainz.
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