The Brazil midfielder travelled with Barca to their opening La Liga game of the season - which they lost 1-0 against Athletic Bilbao - but was left out of the matchday squad. "We had very good talks and I also want to thank FC Barcelona", Bayern sporting director Hasan Salihamidzic told broadcaster ZDF.
"Only a few details are still to be sorted out".
"I can confirm that there's an agreement in principle in the case of Coutinho's loan [to Bayern]", Barcelona director Guillermo Amor said. "We are very happy that we will bring this player to Bayern".
Coutinho joined Barcelona from Liverpool in January 2018 for an initial 120 million euros ($133 million), plus another 40 million euros in potential add-ons. Sources close to the player confirmed he's expected to travel to Bayern over the weekend for a medical and to finalise his move.
Coutinho has made 75 appearances in all for Barcelona, scoring 21 goals and was part of the side beaten in the semi-finals of the Champions League by the eventual winners Liverpool. "He is in the newspapers every day and I don't think we should get into it now".
Barcelona were beaten by a spectacular, last-minute victor from the Bilbao substitute Aritz Aduriz.
Although the signings may block Singh's path, they should provide a much-needed boost for the stuttering Bayern, who only managed to salvage a draw in their season opener.
Three minutes later, Hertha took the lead in curious fashion after Marko Grujic clashed heads with new Bayern signing Benjamin Pavard.