The 26-year-old has entered the final year of his contract and talks with the Bundesliga champions to extend his deal have stalled.
Goretzka is currently unhappy with the wages he has been offered and is demanding a contract worth around £19.5m per year, a similar deal offered to David Alaba before he agreed to join Real Madrid.
However, Bayern are only prepared to offer the German a deal worth around half this figure per season, leaving Goretzka to now consider his options elsewhere.
According to AS, United would be interested in signing the midfielder if he were to become a free agent next summer, though Real Madrid are the latest club to have expressed their interest.
Goretzka made 32 appearances across all competitions for Bayern last season, scoring nine goals and providing eight assists. body check tags ::