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But Chelsea still face strong competition from Barcelona, who are ready to sell a stake in their merchandising arm to finance a move for the 23-year-old.
Sevilla would prefer to sell to Chelsea over Barcelona so they do not strengthen a LaLiga rival.
Kounde has already agreed personal terms on a five-year contract at Stamford Bridge but he is yet to reveal his preference to either of his two suitors.
The France international would be a major signing for Thomas Tuchel as he targets two more new centre-backs after Chelsea sealed a £33m deal for Kalidou Koulibaly.
Chelsea also remain in talks with Paris Saint-Germain over a possible £50m move for Presnel Kimpembe.
The arrivals of Kounde and Kimpembe could allow Cesar Azpilicueta to move to Barcelona, who have already offered him a lucrative two-year contract that he wants to accept.
Initially, the Blues asked for a £7m fee from Barcelona for their captain but it could be negotiated down over time.
In pictures | Chelsea face Charlotte in pre-season
Marcos Alonso is also in talks with Barcelona, with Tuchel interested in adding a wing-back amid the interest in his two Spanish defenders.
Any further signings will depend on player sales, with Kepa Arrizabalaga now attracting interest from Napoli.
In addition, Chelsea are set to complete the signing of 18-year-old full back Zak Sturge from Brighton.