The talented Lyon play-maker almost joined Liverpool last summer but the move collapsed at the eleventh hour.
Now it appears that the Spanish giants want Fekir and are willing to offer a sizeable deal to try and prise the player away from Lyon in January.
Fekir is contracted with Lyon until 2020 and the club are reportedly worried about seeing the player leave for nothing. With such transfer interest, they could be tempted by an offer from either Real Madrid or Chelsea.
Maurizio Sarri reportedly wants Fekir in case Eden Hazard leaves Stamford Bridge next summer. The Chelsea boss has built his midfield around Jorginho, the Brazilian he brought with him from Napoli, but Fekir offers a different kind of threat.
Fekir was linked with Real Madrid in the summer but the club's transfer plans were shelved when Zinedine Zidane surprisingly resigned just days after he led them to the Champions League with a Final win over Liverpool.
Real Madrid's interest in the player has been reignited after Fekir's impressive performances in the Champions League. They see him as an eventual replacement for Croatian star Luka Modric who many expect to move to Serie A next summer.
Fekir was also on the radar of Barcelona but their top target is Ajax midfielder Frenkie de Jong, a player who is also admired by Manchester City and PSG.
The Lyon fans would be sad to lose Fekir with the knock out stages of the Champions League to come but given they run the risk of losing him for nothing at the end of his contract, a January or summer transfer window move is not out of the question.