The 20-year-old has been a regular for Leverkusen since he was 17 but last season was a breakthrough campaign for the midfielder as he bagged 20 goals in 42 appearances.
Havertz already has six Germany caps to his name and scored his maiden goal for his country in their 2-2 draw with Argentina earlier this week.
Such form has naturally seen him linked with a move to the Premier League and compatriot Jurgen Klopp is believed to be a huge fan of the midfielder.
United boss Ole Gunnar Solskjaer is desperate to strengthen his midfield following the departures of Marouane Fellaini and Ander Herrera.