Chelsea are reported to be in advanced discussions over a deal for the 22-year-old, although Sevilla are holding out for a fee of £68m should the Blues opt for a straight-cash sum.
Part-exchange deals involving either Andreas Christensen or Kurt Zouma have also been mooted, and journalist Duncan Castles now claims that Kounde is willing to make the switch to Stamford Bridge after agreeing personal terms with the Blues.
Speaking on the Transfer Window Podcast, Castles said: "As we said on Tuesday, the personal terms have been agreed between Kounde and Chelsea.
"He's happy to move to Chelsea. We've been saying for a while his preference would be Real Madrid but Real Madrid have not entered or made a bid for the player. Sevilla want to sell but only at the right level. A straight cash deal will be difficult and Chelsea have been offering players in addition to cash to Sevilla.
"One of the players they've offered is Kurt Zouma. Usually, when you do these part-exchange deals, they're more complicated because you have to get the player [Zouma] on board and that is going to be a question here.
"The noises coming from around Zouma is that he would prefer to stay in England and in London. At present, the brief from his camp is that West Ham would be more interesting to him than Sevilla.
"From the club side, the guidance I have is that it actually suits Sevilla to get a defender in in part-exchange for Kounde as opposed to cash. It's because of the La Liga spending limitations that are hitting every club at present.
"If Chelsea can provide Sevilla with the right player, and I'm told Kurt Zouma is a player they'd be interested in taking, who will fit straight into the team and be a replacement in the squad, it helps Sevilla in terms of making and accessing La Liga spend limits.
"I'm told Chelsea have an advantage if they can get a player like Zouma or one of their other defenders that Sevilla might be interested in to move there because in this particular case because a cash-plus-player deal is more attractive than a straight cash offer."
Kounde - who has already won one Europa League crown during his time with Sevilla - scored four goals in 49 games across all competitions last season and was rewarded with a place in France's Euro 2020 squad.