Maier, 19, is regarded as one of the most promising teenagers in the Bundesliga and made history by becoming the youngest player to feature for Hertha at the end of the 2016/17 campaign aged just 17.
The highly-rated midfielder went on to make 21 appearances last term and has had a strong start this campaign, catching the attention of Europes elite clubs.
According to the Sunday Mirror, both United and Arsenal have sent scouts to watch Maier in action this season.
Its understood Serie A giants Juventus are also interested in signing the Germany Under-21 international.
In Germany, Maier is already being likened to World Cup-winning midfielder Toni Kroos.
Maier has been tipped for the top since starring for Herthas youth side, providing a large number of goals and assists before breaking into the first-team.
The youngster has a £10million release clause in his current contract which expires in the summer of 2022.