Having failed to impress in his 18-month spell in Spain with Barcelona, Coutinho was shipped out on loan to the Bundesliga club in August.
According to Spanish newspaper AS, Coutinho, the Brazil international, has no future at the Nou Camp and Bayern reportedly have the option to sign him permanently next summer.
Coutinho is rediscovering his best form with Bayern, scoring twice and assisting a further two goals in his first six appearances; he also provided an assist in their 7-2 Champions League thrashing of Tottenham.
Earlier this year, talkSPORT revealed Coutinho would have considered returning to Liverpool on loan, after rejecting a move to Premier League rivals Tottenham.
Coutinho joined Liverpool from Inter in 2013 for a bargain £8.5m, and in 201 games scored 54 goals, before moving to Barcelona in January 2018 for £142m.