The Brazil international has struggled to live up to his £142m price tag since joining from Liverpool in January 2018.
The La Liga champions also offered him to PSG as part of a proposed package which they hoped would see Neymar move in the opposite direction.
Bayern have now expressed an interest in taking the Brazilian on a year-long loan with an end-of-season purchase clause.
Coutinho has scored 21 goals in 75 appearances during his time at the Camp Nou.
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