The 28-year-old has spent the entire 2019-20 campaign on loan with the German giants so far, helping them to an eighth successive Bundesliga title with eight goals and six assists in 23 top-flight outings.
The Bundesliga season is now over, but Bayern will be in Champions League action in August, while they also have the DFB-Pokal final to compete in on Saturday.
Marca reports that they have now struck a deal with Barcelona and Coutinho to keep him at the club until the end of the campaign, with his previous loan terms expiring at the end of June.
The Brazilian has agreed to take a 50% pay cut during that time in order to help Bayern's treble bid, but he is still expected to return to Barcelona after the end terms end, with Bayern having turned down the chance to sign him permanently for £108m.
The Bavarian giants have instead opted to move for Leroy Sane, who is close to finalising his switch from Manchester City.
Coutinho's future beyond the end of the campaign remains uncertain, with Barcelona desperate to offload him in order to trim their wage bill and a move back to the Premier League heavily rumoured.