The France international is understood to be Thomas Tuchel's leading centre-back target in the last knockings of the transfer window, and the Blues have supposedly stepped up their interest in recent days.
A recent report claimed that Chelsea were closing in on the signing of Kounde for a fee of £42.8m, but Sevilla president Jose Castro has insisted that the club are yet to receive a "concrete offer" for the 22-year-old.
Speaking to reporters, Castro said: "It is true that there was an offer for Kounde that we turned down. Right now there is no concrete offer for the player.
"If it comes, we will look at it as we always have done. If we have to [sell], we will do, as long as those resources can be re-invested in the club to keep improving and expand our trophy cabinet.
"While the market is open, anything can happen. We have players who could leave. Anything can happen this time of year until the 31st. It is a window where there have been few moves in most clubs, but not in ours."
Chelsea will likely have to offload Kurt Zouma to West Ham United before they can move for Kounde, but there have been conflicting reports as to whether the Hammers will be able to get a deal over the line.