It means the Blues may have to turn their attentions elsewhere as they look to replace both Antonio Rudiger and Andreas Christensen.
Rudiger, 29, joined Real Madrid on a free transfer following the expiry of his contact.
Christensen has also left the club, and is expected to sign for Barcelona.
Chelsea were hopeful of securing a move for France international Kounde, 23, and were set to activate his £69million release clause.
However, the player aggravated the issue on international duty in France's recent 1-0 defeat to Croatia, and may have missed the opportunity to secure a lucrative move to Stamford Bridge this summer.
The Blues could look elsewhere in the market for suitable centre-back options.
talkSPORT takes a look at who they could target instead of Kounde should they end their interest.
Milan Skriniar (Inter Milan)
Having featured 215 times for Inter Milan to date in all competitions, Skriniar has become one of the standout centre-back's in European football.
The Slovakia international, 27, is also a target for both Tottenham and Paris Saint-Germain, but Chelsea could have the edge with Romelu Lukaku likely to head to the San Siro this summer and form part of the deal.
Inter are said to be looking for around £60-68million for their star defender, but are believed to be open to reducing their asking price to just £50m.
Pau Torres (Villarreal)
Torres, 25, has previously been linked with a move to Tottenham and Manchester United.
It remains to be seen where the Spain international will be playing his football next season, but Chelsea do have the advantage over the Red Devils given they can offer Champions League football.
The player is valued at around £55million, and with plenty of interested parties, the Blues would have to act fast if they are to capture the Spaniard.
Kalidou Koulibaly (Napoli)
The Senegalese colossus joined Napoli in 2014 and has spent eight seasons with the Serie A club having joined from Genk.
He has established himself as one of the top defenders in the world, and last season helped his side to third in the Italian top flight.
The 30-year-old appeared in 34 games in the league last campaign, scoring three goals and assisting on three occasions.
With his contract up next summer, Napoli could be persuaded to part ways with him on the cheap, or risk losing him for free at the end of next season.
Matthijs de Ligt (Juventus)
Another name Chelsea could turn to is Juventus star De Ligt, who they have recently been linked with.
The 22-year-old would be an excellent replacement for Rudiger, considering he has similar defensive qualities, and has a wealth of experience already.
Similar to the German, De Ligt is strong in the air and likes to clear his lines. He does not get into regular tackles, but makes up for it by winning duels.
Manchester United, Manchester City, Real Madrid and Paris Saint-Germain have all previously been linked with the Dutchman.
Gleison Bremer (Torino)
Another star plying his trade in Turin is Brazilian defender Bremer of Torino.
The Italian side would likely entertain a bid in the region of £34m for their star.
Bremer has had an outstanding season in which he has established himself as one of the league's best defenders, and was deservedly crowned the Serie A Defender of the Year.
Having made over 100 appearances for Torino since joining the club from Atletico Mineiro in 2018, now could be the time for the centre-back to make the next step, so could Stamford Bridge be his next destination?