Reports carried in France claim Claudio Ranieri's side have lodged a £13m offer for Kondogbia, who's been linked with Chelsea, Manchester United and Real Madrid as well as Arsenal.
The 21-year-old defensive midfielder was excellent against United during Sevilla's 3-1 victory over David Moyes's side at Rio Ferdinand's testimonial.
The Old Trafford side reportedly retain an interest in the Frenchman, although Arsenal are believed to be the Premier League side most likely to move for him.
So it comes as a blow to learn that Monaco are keen to offer him a route back to his native France. The youngster made the move to Sevilla last season from Lens, and impressed during a strong debut campaign in La Liga.
Sevilla have previously insisted that Kondogbia will not be allowed to depart for anything less than his release clause - reportedly worth around £17m.
Monaco obviously hope Sevilla will negotiate, but the fact they haven't matched the valuation leaves the door open for Arsenal or Manchester United to outbid the big-spending French club.
But they may have to move quickly, with Juventus reportedly the latest club to register an interest in the talented midfielder.
He only made his full debut for France earlier this month, but Juventus are allegedly impressed by his rapid development and stand to challenge Monaco, Arsenal and United for his signature.