Arsenal are believed to be interested in signing the 20-year-old having reportedly tracked the midfielder for the past 18 months.
Unai Emery is looking to find a replacement for the outgoing Aaron Ramsey and sees Aouar as an ideal candidate, but Lyon have no intention of selling.
Liverpool and Manchester City are also said to be keen on Aouar, but Lyon president Jean-Michel Aulas has dismissed rumours that Aouar could leave the club in the near future, and not even the reported £63million value of the player would tempt the club to sell their prized asset at that price:
“A departure for Houssem Aouar? The door is totally closed for our most successful hope.
“He has come from the academy and I think he is the future of Lyon.
“There will be very few departures this winter. We are not planning to let the world go this summer, we want to keep our players.
“The potential buyers will have to be convincing, they will have to have the right arguments and I do not see many of them at the moment.”
Aouar has previously stated that he wants to remain at Lyon for now but has not ruled anything out in the future.
The midfielder has made 21 appearances in all competitions and has scored five goals and assisted four so far this season.