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The 21-year-old midfielder has been hotly linked with a move away from the club in the summer. He starred in their Champions League last-16 first-leg victory over Juventus on Wednesday, creating Lucas Tousart's winning goal.
Having previously shone at the highest level, a raft of clubs are interested in his signature, with Real Madrid, Manchester City, Juventus and Paris Saint-Germain on a list that seemed to be headed by Chelsea in January.
"I'm not thinking about by future," he told TF1 show 'Telefoot'. "I'd rather think about the weeks to come. They will be important for Lyon and for us.
"I still have a lot to bring to the team and I'm trying not to pollute my mind by staying focused on what happens on the park."
He was delighted with the team's performance against Juve but has urged his cohorts to stay focused ahead of what promises to be a difficult encounter in Turin in little over a fortnight.
"No-one saw us playing a match like that but we did it," he said. "We had belief from the start and collectively we surpassed ourselves.
"We can't get carried away. I think that we've given ourselves a chance and we're going to try to play our game and not to defend because if we do that, it could get very complicated."
In the meantime, he is focused on Sunday's derby encounter against Saint-Etienne, which promises to be an explosive affair, with Lyon seeking to climb out of their mid-table position and Claude Puel's men simply fighting to stay afloat in the league.
"We have to win this match," he said. "There's going to be a lot at stake, even if neither side is where they should be in the league."
Aouar has played 130 matches for Lyon's first team, scoring 24 goals and laying on the same number of assists.
It is anticipated that when he is sold in the summer, his fee will surpass that of Tanguy Ndombele, whose ?55 million ($69m) move to Tottenham last summer, was a club record.