The European champions currently have Kurt Zouma (26), Andreas Christensen (25), Antonio Rüdiger (28) and Thiago Silva (35) as central defending options.
But it seems Blues boss Thomas Tuchel is not wholly convinced.
As a result, Chelsea are pressing to get the signature of the highly in-demand central defender Kounde.
According to Fabrizio Romano, the offer is around €30m, including Zouma going to Sevilla.
“Chelsea and Sevilla are discussing to reach an agreement for Jules Koundé/Kurt Zouma swap deal.
“Talks progressing – Chelsea now offering around €30/35m and Zouma included in the negotiation.
“Personal terms are not a problem for Koundé who’s waiting to join Chelsea,” the Italian reporter posted on Twitter.
Tuchel’s side take on the Europa League champions Villarreal in the UEFA Super Cup on 11 August.