Despite his status at the Ligue 1 outfit, the 22-year-old may be allowed to leave this summer if his club do not win the Champions League.
That scenario has been created due to the financial implications of the coronavirus pandemic and Lyon missing out on European qualification through France's top flight.
According to L'Equipe, City boss Pep Guardiola is a big admirer of the 22-year-old, who allegedly possesses an asking price of £54m.
However, City may prioritise other areas of the pitch this summer, leaving Arsenal and Juventus as other options for the playmaker.
Aouar will hope to impress when Lyon square off against the latter in the Champions League last 16 on Friday night.