The Belgium international is on a season-long loan at Sunderland and has been linked with a permanent move away from Old Trafford.
The Ligue 1 side have been one of the teams credited with an interest in Januzaj and his representative, Dirk Devriese, verified that talks have taken place.
However, he is yet to hear from United that they definitely want to sell the 21-year-old.
"Lyon are one of the many French clubs who have recently sounded out Adnan's plans," Devriese told HLN.
"Out of respect, we to listen to everyone. However, the ultimate decision is with Manchester United and we have not heard from them that the club wants to sell Adnan.
Januzaj, who had an unsuccessful loan spell with Borussia Dortmund last season, has played 15 matches for Sunderland across all competitions, scoring once.