After Bayern's 2-0 DFB-Pokal semi-final victory in Leverkusen, Neuer told Sky: "I am not going to announce anything yet. But things are looking good at the moment."
The 40-year-old continued: "It is not only about the players on the pitch but about the whole squad and the club. You can feel that something has evolved.
"This is the second season with Vincent Kompany. We all benefit from each other. Right now, we are having a really good time."
Bild reports that the Bayern hierarchy is encouraged by those words, viewing them as a positive signal that the club's long-serving captain may commit to at least one more season.
Bayern are prepared to offer a further extension and are not rushing him toward a decision.
A treble remains possible for the club this season. Whether Neuer sees that through as part of the next chapter, or as the perfect farewell, is the question the club is waiting to have answered.