According to a report in the Daily Mail, the Ligue 1 side is keen to bring in both players during the January transfer window, but they are likely to want to sign them on lower wages than they currently have.
Januzaj, who not long ago was hailed as a rising star in Belgium, is on a season loan to Sunderland but would not object to a permanent move as he does not believe he has a future at United under Jose Mourinho.
The Dutchman Depay on the other hand is reportedly valued at £15million by United.
If that price tag proves too high for Lyon, another possible suitor for the 22-year-old could be Everton, as manager Ronald Koeman is believed to be an admirer of his young compatriot.