The Blues have long been linked with a move for the versatile France international, who is capable of playing in the heart of defence or at right-back.
Chelsea tried and failed to prise Kounde away from Sevilla in January, with the 23-year-old ultimately staying put to help Julen Lopetegui's side qualify for the Champions League.
However, Chelsea were always expected to reignite their interest in the former Bordeaux man, and the Blues are now said to have agreed a £55m deal to bring him to Stamford Bridge.
News of an agreement for Kounde followed confirmation that the centre-back was taking part in pre-season training alone, although he is working his way back from a hernia operation.
Now, the player himself has all but confirmed that he will be heading for the exit door at Sevilla after stopping to greet a group of supporters at the club's training facilities.
Kounde was approached by one fan who said: "Good luck wherever you go, have a great time," to which the Frenchman simply responded: "Thank you".
Another supporter then pleaded with Kounde not to make a move to Barcelona, who are believed to be Chelsea's main rivals in the race for his services, but the centre-back did not respond.
Barcelona have supposedly urged Kounde to rebuff interest from Chelsea and remain in La Liga with Xavi's side, but Sevilla would prefer to sell to the Blues rather than a direct domestic rival.
Kounde is already said to be house-hunting in London while negotiations rumble on in the background, and personal terms are not expected to pose an issue.
The 5ft 10in defender prepares to leave Sevilla after recording nine goals and three assists in 133 appearances for the club in all competitions since arriving from Bordeaux in 2019 for £22.5m.
Kounde helped Sevilla win the Europa League in his debut season at Los Palanganas, and he has already won the Nations League since breaking into the France squad.
Chelsea have already brought in Kalidou Koulibaly to beef up their defence this summer, with Andreas Christensen and Antonio Rudiger departing for Barcelona and Real Madrid respectively.
Kounde's arrival could also open the door for Cesar Azpilicueta to leave, with the Spaniard said to be increasingly confident of sealing a summer switch to Barcelona.
La Blaugrana have supposedly drawn up a five-man list of alternatives to Kounde, including the likes of Arsenal's William Saliba and Inter Milan's Milan Skriniar.