There has been known mutual admiration between Real Madrid boss Zinedine Zidane and the young forward, with Fekir being quoted last summer “If Zizou called, I would be there tomorrow.”
The 24-year-old has been compared to Zidane because of his silky style of playing and great vision, something Arsenal have been missing since Santi Cazorla got sidelined with a serious foot problem in October last year.
And with the likely departures of Mesut Ozil and Alexis Sanchez in January, Fekir is deemed as an ideal replacement.
The forward has been impressive this season with nine goals and four assists so far as Lyon sit third in Ligue 1.
Fekir is currently tied to Lyon until 2020 and is evaluated at around £50 million.