The former Liverpool star has struggled to make an impact in Spain since leaving Anfield 18 months ago.
Coutinho has always insisted he wants to stay and fight for his place at Barcelona.
But according to journalist Bruno Andrade, the Brazilian will soon be shipped out.
He claims Coutinho will be loaned to Bayern Munich, who will have an option to buy him outright at the end of the deal.
The Bundesliga champions will have to pay Coutinho’s €11m (£10.1m) annual salary and are now in talks with the midfielder’s representatives.
PSG remain interested in Coutinho’s signature as they prepare to lose Neymar.
The fellow Brazilian is expected to re-join Barcelona this summer and could be swapped with his international team-mate.
“Neymar can leave PSG, if there is an offer that suits everyone,” PSG chief Leonardo told La Parisien.
“But to date, we do not know if anyone wants to buy him, or at what price.
“All this is not done in a day, that’s for sure.
“PSG wants to rely on players who want to stay and build something big. We do not need players who would do a favour at the club by staying here.”
According to journalist Tancredi Palmeri, Barca are willing to offer the Ligue 1 champions £92m and Coutinho in order to bring Neymar back.
“Barcelona ready to offer Coutinho + 100m€ [£92m] for Neymar,” he said on Twitter.