A host of clubs have been linked with Kondogbia, who caught the eye at Sevilla last season with a number of impressive performances.
The likes of Real Madrid and Chelsea have been credited with an interest in the 20-year-old as they look to bolster their midfield options.
Real are believed to have cooled their interest in Kondogbia as they pursue a deal in Real Sociedad's Asier Illarramendi, who has been mentioned as a possible target.
Arsenal boss Arsene Wenger is believed to be in the market for a new defensive midfielder and Kondogbia is understood to be on his radar.
Sevilla are battling to keep hold of their best stars this summer after failing to qualify for Europe next season and Arsenal are ready to test their resolve to retain Kondogbia.