The France international has emerged into one of Europe's brightest defensive prospects after becoming a regular for Julen Lopetegui's Palanganas since arriving from Bordeaux in 2019.
Kounde won the 2019-20 Europa League with Sevilla and has already made 133 appearances for the club in all tournaments, scoring nine goals and providing three assists.
The 2021-22 season saw Kounde register three goals and an assist in 44 matches to help Sevilla maintain a title challenge in La Liga, where he remained after Chelsea's failed attempts to sign him last summer.
Following Todd Boehly's successful takeover, Chelsea have been expected to reignite their interest in Kounde, whose contract with Sevilla expires in two years' time.
However, the Blues could ultimately concede defeat in the race for Kounde, who is intent on joining Barcelona this summer, according to Mundo Deportivo.
The report claims that Sevilla will not stand in Kounde's way of leaving if the right offer arrives, but Barcelona can still expect to be quoted as much as €65m (£55.8m) for the 23-year-old.
In order to drive the price down amid their financial woes, Barcelona could supposedly include at least one player in a part-exchange deal, but no specific names have been mentioned.
Nevertheless, there is said to be 'great optimism' that Barcelona will be able to agree a deal with Sevilla, and Chelsea are aware of the defender's intention to play for the Blaugrana.
Christensen will officially leave Chelsea on a free transfer at the end of the month alongside Antonio Rudiger, who has signed a four-year deal at Real Madrid.
Rudiger revealed at his Real Madrid unveiling that he had turned down an offer from Barcelona to join Los Blancos, but Barcelona could still raid Chelsea's defence further.
Alonso has revealed his desire to play in La Liga, but Chelsea boss Thomas Tuchel is understood to want Azpilicueta - who currently captains the first team - to stay at the club.