The 40-year-old goalkeeper says he has no concrete plans yet for life after playing, but that has not stopped clubs from thinking ahead.
In a joint interview with Bild, Bayern Munich president Herbert Hainer and Schalke supervisory board chairman Axel Hefer both confirmed they would welcome the long-serving Germany international back in some capacity once his career ends.
Neuer's contract at Bayern runs until the end of the season, with no final decision yet made on whether he will extend for a further year. Born in Gelsenkirchen, Neuer began his career at Schalke before joining Bayern in 2011, giving both clubs a legitimate claim on his future.
"Of course it is our wish to involve former players in the future too, if they are ready for it," Hainer said.
"Should Manuel actually stop, he would certainly take some time to catch his breath first. And then he will surely look at what he would like to do.
"Then we need to have that conversation."
Hefer made the case for a return to his boyhood club.
"His departure was controversial, but personally I think everyone can make mistakes, especially when they are young," he said. "That is something you can move on from eventually. I see it like Mr Hainer does: he will enjoy his time first and then think about what he wants to do.
"Whether he then wants to work in his old or his new home — that is something he has to decide for himself."
Neuer left Schalke for Bayern in an initial move that was met with anger from some sections of the Gelsenkirchen support at the time, given his boyhood connection to the club. He has since won a string of major honours in Munich, including the Champions League, and remains Germany's first-choice goalkeeper.
The comments from Hainer and Hefer suggest neither club is willing to rule itself out of Neuer's post-playing plans, even at this early stage. Both were careful to stress that any decision rests entirely with the goalkeeper himself, and that no approach would be made until he has had time away from the game to consider his options.
For now, Neuer remains focused on adding to his trophy collection in what could be his final season between the posts, with Bayern once again among the favourites for major honours both domestically and in Europe.