However, sporting director Christoph Freund moved to cool the reports at a press conference on Friday, saying he had not yet held a formal discussion with Neuer about his future.
"This is the first time I've heard this. There has not yet been a discussion with him," Freund told journalists in Mainz.
The contradiction mirrors the cautious approach both parties have taken throughout the negotiations. Neuer originally indicated he would make a decision around his birthday in March, then asked for more time.
His comments after the DFB-Pokal semi-final win over Bayer Leverkusen — where he produced a world-class save to deny Nathan Tella — were widely read as a positive signal.
If Neuer agrees, the extension would allow Jonas Urbig, 22, to continue his development as heir apparent while Neuer remains the undisputed number one for one further season.
Bayern's pursuit of Daniel Heuer Fernandes from Hamburger SV as a potential backup continues in parallel, though that move would only be activated if Neuer confirms his retirement.