The France international is expected to leave Sevilla this summer and has been hopeful of moving to Chelsea.
But the London club's ownership saga has stalled negotiations and opened the door to rivals, including Barca.
Mundo Deportivo says Barca coach Xavi is a fan of Kounde, which is something that has flattered the stopper.
Further encouraging Barca is Xavi's good relationship with Sevilla sporting director Fernando Navarro.
However, a stumbling block is likely to be Sevilla's valuation, as they're seeking at least €90m to sell the young defender.
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