The Polish striker was unhappy with the salary offered by Bayern and had clashed with the Bavarian club's coach Julian Nagelsmann over tactical choices.
The Poland striker, who has been linked with a move to Barcelona, said at a news conference that a transfer would be the best outcome for all sides.
Coach Mauricio Pochettino was manager of Tottenham in the Premier League for five years and led the Spurs to the Champions League final in 2019.
Javi Martinez headed in the winning goal in extra time as Bayern Munich beat Sevilla 2-1 in the UEFA Super Cup in a stadium partially filled with fans.
Football players in Germany contemplate staging collective protests following the police killing of unarmed black man George Floyd in the United States.
Professional football resumed in Germany after a two-month break with four games in the second division taking place behind closed doors, and South Korea midfielder Lee Jae-sung scored the first goal in the division.
Chelsea will need another Munich miracle in the second leg on March 18 to overturn the deficit at the Allianz Arena, where they famously beat the German club in the 2012 Champions League final.
German police confirmed that four visiting Bayern Munich fans have been injured during an attack by suspected Olympiakos supporters ahead of the two clubs' Champions League match.
Although Coutinho failed to live up to expectations after joining Barcelona in January 2018 for a club-record transfer from Liverpool worth 160 million euros (then $192 million), his arrival in Germany has also been welcomed by Bayern's club rivals.
Coutinho, 27, joined Barcelona from Liverpool in January 2018 for a club-record fee of $133 million plus $50 million in variables.
35 year old Arjen Robben has decided to put an end to his storied career after quitting Bayern Munich.
In basketball action, Turkey's Anadolu Efes defeated Germany's Bayern Munich 92-77 in the 16th round of the 2018-19 Turkish Airlines EuroLeague regular season on Thursday night.
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