Neuer was limited to 38 appearances in all competitions in 2018-19 as the German side edged ahead of Borussia Dortmund in the league by two points but crashed out of Europe in the early stages.
However, they have waved goodbye to one veteran in centre-back Mats Hummels, who returned to Borussia Dortmund, while wing duo Arjen Robben and Franck Ribery left at the expiry of their contracts last month.
Although Neuer is tied to the club until 2021, agent Thomas Kroth says the 33-year-old is worried Bayern have fallen too far behind their continental rivals and will consider leaving to achieve his dream of winning the Champions League again.
"Manuel is success-oriented. My impression is that the gap to the top four English top teams is already serious and the Munich squad is currently not yet as competitive or set up to tackle Manuel's goals seriously.
"When he realises that Bayern are responding, then he will probably blossom again.
"He does not want to retire in 2021. Now he is in the phase in which he has to decide: how will things progress in the future?
"Signing a contract extension and ending his career at Bayern is of course the obvious option, but it's not the only one."
Neuer has faced criticism for his sub-par performances for Germany and Bayern over the last year, but Kroth is not concerned about his form, inisisting he is still at his best.
"Much has been said and interpreted against him," Kroth said. "The bottom line was: 'He's 33 years old now and he's starting to break down'.
"Many have interpreted his achievements as having lost the extraordinary and invincible ability."
Bayern begin their 2019-20 season preparations with a friendly against Arsenal on Wednesday July 17 in California, USA.