The Gunners are looking to bring in reinforcements this summer to boost their Champions League hopes for next season.
After narrowly missing out on a place in Europe’s top club competition last time around, boss Unai Emery has been left with a much smaller transfer budget than he would have liked.
Unless current players on the books are sold to boost the budget, there will only be around £40m to spend on new ones.
Crystal Palace star Wilfried Zaha is being heavily linked with a move across London but the two clubs may never be able to agree on a transfer fee.
That is after reports that that Arsenal are ready to offer £40m for the Ivory Coast man, half of the £80m that Palace are believed to want.
Zaha, a boyhood Gunners fan, wants the move but the Emirates club look like being priced out of any deal.
Arsenal may have been offered a cheaper alternative though, with Fekir now emerging as a possible signing.
According to the Daily Mirror, Lyon have invited the club to buy the France international for a cut-price fee.
The 25-year-old nearly signed for Liverpool last summer but the deal broke at the last minute after a failed a medical.
Fekir is keen to move to the Premier League and has been told that he can leave the Ligue 1 outfit this summer.
Former Lyon manager Bruno Genesio recently spoke out about the midfielder’s frustration at the transfer to Liverpool breaking down.
“I think that he [Fekir] was very frustrated with his cancelled transfer to Liverpool at the beginning of the season,” Genesio told French radio station RMC.
“He made the World Cup, he had some injuries. He certainly did not feel strong enough to take on the role of leader, which he had done the previous season, relaying technical information on the pitch.
“Nabil is coming to the end of a cycle in Lyon. He has experienced a lot of things here.
“I think that he needs a new challenge, to push his limits, and to be self-critical. Because we know, we always need a personal challenge in a career, and to ask questions of ourselves.”
Fekir was part of France’s World Cup winning squad at last summer’s World Cup in Russia.