It had looked very likely that the centre-back would become the Blues' second high-profile signing of the summer after Romelu Lukaku, with Thomas Tuchel eager to bolster his defensive options.
Chelsea believed that they had a verbal agreement in place to sign Kounde for around €50m (£42.8m).
However, The Athletic reports that Sevilla have now requested €15 million (£12.8 million) more than the fee originally discussed, which Chelsea are not prepared to pay.
The report suggests that the Spanish side have had a change of heart after seeing Chelsea receive £29.8m for Kurt Zouma's sale to West Ham United, while they are also worried about not being able to sign a suitable replacement before the transfer deadline.
Kounde did not feature in Sevilla's squad for their 1-1 draw with Elche in La Liga on Saturday.