The Frenchman, who was part of his country's U20 World Cup-winning team, has supposedly attracted interest from a number of Premier League clubs including Arsenal and Chelsea.
However, the 20-year-old looks as if he will move to the Stade Louis II after La Parisien claimed that the club were in contact with the player's agent.
While Sevilla aren't thought to be keen on letting Kondogbia go, it is alleged that the player has a £15m release cause in his contract, and they are resigned to losing their man after brining in Stephane Mbia on loan from Queens Park Rangers.
Kondogbia's agent is reported to have flown into Monaco on Monday to discuss a move for his client, and the Ligue 1 outfit are hoping to have made a decision on by Tuesday.
Kondogbia earned his first full international cap against Belgium earlier this month.