Bard, 19, is a France under-20 international and made one Ligue 1 appearance for OL this season.
His performances in the UEFA Youth League, which included two assists against Manchester City, caught the eye.
And Bundesliga champions Bayern have initiated ‘concrete talks’ to sign Bard, L’Equipe reveals.
French clubs Lorient, Brest, Nice and Reims have recently shown interest in the OL academy product.
Bard currently has a contract that runs until 2022 at the Groupama Stadium.
Bayern would like to present a medium-term project to Bard, which would see him start in their B team.