The Blues had been in talks with Manchester City over a return for Ake, but it is understood that discussions have now been broken down, with the Netherlands international set to stay with the Citizens.
Chelsea are believed to be on the verge of signing Kalidou Koulibaly from Napoli, but they are targeting another high-profile centre-back, as both Andreas Christensen and Antonio Rudiger have left the club this summer.
According to the Evening Standard, having missed out on Ake, Thomas Tuchel's side will revive their interest in Kounde, who is said to be pushing to leave Sevilla this summer.
Paris Saint-Germain's Presnel Kimpembe and Juventus's Matthijs de Ligt have also been linked with moves to Stamford Bridge over the last few weeks.
Man City have also been credited with an interest in Kounde, while Barcelona are believed to be long-term admirers of the Frenchman, with the La Liga outfit still said to be in the race.
Kounde was again in strong form for Julen Lopetegui's side during the 2021-22 campaign, making 44 appearances in all competitions, contributing three goals and one assist in the process.
The centre-back still has two years left to run on his contract at Estadio Ramon, but he is looking to leave the La Liga outfit during this summer's transfer window in search of pastures new.
Sevilla are said to value Kounde in the region of £55m, though, and it is unclear whether Tuchel's side would be prepared to pay that figure for the defender considering the imminent arrival of Koulibaly.
Sevilla chief Jose Maria Cruz recently admitted that Kounde is keen to leave the club this summer for a fresh challenge.
"Again, the player, I am sure, respects Sevilla FC. He is happy with us. In the case of Kounde, it is not a matter of money. It's a matter of him wanting to play in a more competitive team than Sevilla FC," he told Sport Witness.
"I am sure he is a player that is attractive for teams like Chelsea, FC Barcelona, Bayern Munich and these types of teams. He wants to play in a more competitive team.
"It's the same case we had some years ago with [Clement] Lenglet. He was very happy, but he thought after playing some years at Sevilla FC, he was prepared to go to FC Barcelona.
"The first time we received an offer for him was a season before he was transferred. He [Lenglet] and his father told us they didn't leave Sevilla then because they preferred to stay here and play a lot of matches."
Kounde joined Sevilla from Bordeaux in July 2019, and he has represented the club on 133 occasions in all competitions, contributing nine goals and three assists.