The France international shone as the Ligue 1 heavyweights knocked Arsene Wenger’s Gunners out of the Champions League earlier this season.
Kondogbia scored one of Monaco’s three goals at the Emirates Stadium, which were vital in the away goals aggregate win for his side.
Reports suggest that Inter Milan have already shown an interest in the player, but that Arsenal are very much in the running.
Although Monaco are keen to keep him, a fee in the region of €35m could be enough to persuade them to sell up.
The 22-year-old only joined the Stade Louis II club last summer from Sevilla after carving out a reputation as one of La Liga’s top box-to-box talents.
Kondogbia has represented Les Bleus on three occasions after making his debut back in 2013 at the age of 20.