Aouar is a favourite of City boss Pep Guardiola, having impressed at Champions League level with OL.
L'Equipe's Bilel Ghazi revealed on social media: "Even if OL had qualified for a European Cup next season, the deal was already established for Aouar in Lyon.
"To be completely clear, today, Manchester City is still as much a favourite on this Aouar dossier. There are ongoing discussions between City and Aouar. Over the past year, the interest of both parties has not decreased in intensity.
"The price of Aouar's transfer? In the current context, we can think of a transfer of 50-60 million euros."