The goalkeeper has been with the Bavarians for eight years and has made 336 appearances in all competitions to win seven Bundesliga titles, five DFB-Pokals and a Champions League crown, goal.com reported.
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.
Bayern has already signed defenders Lucas Hernandez from Atletico Madrid and Benjamin Pavard from Stuttgart this summer.
However, the German giant has waved goodbye to one veteran in center-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 said the 33-year-old is worried Bayern has fallen too far behind its continental rivals and will consider leaving to achieve his dream of winning the Champions League again.
"He wants to win Euro 2020 and he wants to win the Champions League again," Kroth told Suddeutsche Zeitung.
"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 realizes that Bayern is 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, insisting 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 begins its 2019-20 season preparations with a friendly against Arsenal on Wednesday July 17 in California, the US.