The 19-year-old winger is highly regarded by the Citizens, but he has only made one senior appearance under Pep Guardiola, playing 65 minutes in the 1-0 defeat to Leicester City in the Community Shield last season.
Edozie has caught the eye at youth level for Man City, scoring 13 goals and registering 10 assists in 57 appearances over the last three seasons.
However, journalist Fabrizio Romano claims that the Lewisham-born winger is set to move to Germany and join Leverkusen on an initial two-year deal.
Romano adds that City are willing to let Edozie leave the club as the teenager has no intention of extending his contract, which is due to expire in June 2023.
The Citizens have already allowed promising winger Jayden Braaf to join Borussia Dortmund on a free transfer this summer, while 20-year-old goalkeeper Gavin Bazunu has completed a permanent switch to Southampton.