Aouar was tipped to join Premier League side Arsenal, while the likes of Paris Saint-Germain, Juventus, Manchester City and Real Madrid were also linked.
But the 22-year-old French midfielder will remain with the 2019-20 Champions League semi-finalists this season.
"[Why did I make] my choice to stay in Lyon?" Aouar said after scoring in Lyon's 1-1 Ligue 1 draw against rivals Marseille on Sunday.
"I felt that I could still bring something to this team and to this club.
"That's why I have made the choice to continue my adventure with Lyon. I hope we will get up and find our form again quickly."
Aouar converted a 28th-minute penalty to cancel out Dimitri Payet's opener three minutes earlier as Lyon and 10-man Marseille shared the spoils.
Lyon have struggled for form since their memorable run in the Champions League last season, managing just one win from six Ligue 1 fixtures this term to sit 14th in the table.
"We are very disappointed that we did not pick up the three points. This is really what we had to do. We had to win, especially after our recent results.
"I find it hard to explain why we were not better up front. We can make the gap but we miss the right pass or the right shot. It is something that must be improved as quickly as possible. It is not normal for us."