The first leg will be played at Old Trafford on Tuesday 7 January, with kick-off at 8pm.
And the return leg at the Etihad is scheduled for Wednesday 29 January at 7.45pm.
City are looking to win the competition for third-successive season having triumphed in 2018 and 2019.
Ticket information for both matches will follow in due course.
City's FA Youth Cup Third Round clash against Swansea City will be available to watch via the Man City for TV app.
For more information on how to watch, visit the Man City for TV website.