Neuer is widely regarded as the finest goalkeeper in world football.
The Germany international won the World Cup in 2014 and has helped Bayern win the league every year for the past four seasons.
Manchester City are on the lookout for a new No1 given Claudio Bravo's erratic form.
Bravo has toiled at the Etihad since joining from Barcelona in the summer and has recently fallen behind Willy Caballero in the pecking order.
Top six Premier League club's goalkeeper save percentages
Thu, January 19, 2017Which top six goalkeeper has the highest save percentage so far this season?
Claudio Bravo (Manchester City) – 28 per cent
And, according to Transfer Market Web, Pep Guardiola is willing to spend big to bring Neuer to the Premier League.
The goalkeeper played under Guardiola for three seasons during their time at Bayern together.
And it is claimed the 30-year-old could be open to a new challenge after six years at the Allianz Arena.
City can offer him higher wages than Bayern but Barcelona could also delve into the market with Marc-Andre Ter Stegen leaving plenty to be desired.
The report says City will also offload Joe Hart in the summer.
Chelsea, Liverpool and West Ham have all been backed to swoop for the England international, who is currently on loan at Torino in Serie A.