Thomas Tuchel's team are desperate to bolster their defence this summer, with two centre-backs set to leave.
Chelsea have identified long-term target Kounde as an ideal replacement.
ABC Sevilla reports Blues chiefs are "convinced" that they can come to an agreement.
The report adds that Chelsea are urging Kounde's agents to resist approaches from other clubs.
Sevilla held out for their star defender's release clause, believed to be around £70million, last summer.
But Chelsea believe they can get him for less this time around.