"There is a clear tendency," Bayern's director of sport Christian Nerlinger told the Sueddeutsche Zeitung daily. "Now it's just a question of how quickly we can find a solution."
Club president Uli Hoeneß meanwhile was reported by several newspapers as having difficulty hiding his optimism that the 25-year-old Neuer will soon be in a Bayern uniform.
"I know what his decision is. We will have to see what happens," he said.
Neuer has said on Saturday he has decided where his future lies – but refused to say where.
"A decision has been taken. People who need to know, know. So everything is cleared up," he said.
His contract at Schalke runs until 2012 and unless he signs an extension the Royal Blues will need to sell him soon or risk losing him on a free transfer in a year's time.
Bayern have struggled to find a suitable replacement since ex-Germany captain Oliver Kahn retired in 2008 and the Munich giants are reported to be ready to pay €20 million ($28.8 million) for Germany's first-choice goalkeeper.
German daily Bild claimed last week Schalke are set to offer Neuer a bumper contract worth €21 million over the next three years, but the club has since denied that.
Neuer has also been linked to Premier League giants Manchester United with Dutch goalkeeper Edwin van der Saar retiring at the end of the season.