The 23-year-old has enjoyed another impressive campaign in the heart of Julen Lopetegui's defence with three goals and an assist from 43 appearances in all competitions this term.
Kounde has featured from the first whistle 30 times in La Liga for Los Palanganas, who only need a point against Athletic Bilbao on Sunday to confirm their top-four finish.
Sevilla resisted attempts to prise Kounde away from the club last summer, but the Spanish outfit will not be in such a strong negotiating position this time around.
Kounde's contract at the club now only has two years left to run, and the France international is widely expected to head elsewhere in the summer transfer window.
Chelsea saw their bid to sign Kounde rebuffed by Sevilla last year, but the Blues are reportedly keen to wrap up an early summer deal for the former Bordeaux man.
However, Mundo Deportivo reports that Barcelona are primed to hijack Chelsea's attempts to lure the Frenchman to North London as part of their defensive reshuffle.
The report adds that Catalan chiefs view Kounde as the perfect long-term partner for Ronald Araujo, but Sevilla are still driving a hard bargain.
Los Palanganas have supposedly not budged on their €80m (£67.7m) asking price, which could lead Barcelona to try to agree a player-plus-cash deal for the Frenchman.
Clement Lenglet and Sergino Dest are two players who could be offered to Sevilla, and Lopetegui's side are believed to be interested in signing the latter.
Meanwhile, Lenglet spent one and a half years at Sevilla before moving to Barcelona in a £32.3m deal in 2018, but the Palanganas are supposedly not keen on the idea of the 26-year-old returning.
Newcastle United are still thought to be in the mix, with the Magpies seeing a €70m (£59.2m) offer turned down in January following their Saudi-backed takeover.
Kounde has amassed nine goals and three assists in 132 games for Sevilla over the past three years, winning the Europa League in the 2019-20 campaign.
Barcelona are rumoured to be in advanced talks with Marcos Alonso and are already set to welcome Andreas Christensen to the club from Chelsea, with the Denmark international out of contract at Stamford Bridge in the summer.
Christensen withdrew from the squad to face Liverpool in the FA Cup final on the morning of the game, and Thomas Tuchel recently admitted that it was "not the first time" such a situation had occured.