The west London club and Crystal Palace have held a fresh round of talks over a potential deal, though the Eagles are insistent they will not let their defender go for a cut price. The 26-year-old played three times for France during their run to the World Cup semi-finals, including in the 6-4 defeat to England in the third-place play-off in Miami on Saturday.
While there is no agreement in place at this stage, Chelsea's spending shows no signs of slowing after their £117m move to sign Morgan Rogers from Aston Villa and their £45m signing of Marco Palestra from Atalanta.
Elsewhere at Stamford Bridge, midfielder Enzo Fernandez has released a statement addressing Argentina's World Cup final defeat, in which he played a significant part.
The defending champions were beaten 1-0 by Spain in East Rutherford, New Jersey on Sunday, with Ferran Torres striking the winner in extra time after Fernandez saw red in second-half stoppage time for a second yellow card.
The Chelsea midfielder had initially been booked by Slovenian referee Slavko Vincic for dissent before being sent off following a late lunge on Pau Cubarsi. He apologised to Argentina supporters as he trudged off, though he let his frustrations show by kicking a pitchside microphone on his way to the dressing rooms.
Fernandez took to Instagram on Monday to address the Argentine fans who had backed Lionel Scaloni's side throughout the tournament.
"As time passes, you realize there is something much bigger than a result. For years, this group has represented our country in the best possible way. It teaches that competing isn't just about winning, but about giving everything for the shirt and never giving up. Being part of this group, which has always stood up, competed to the very end, and defended these colors with pride, humility, and commitment, is something I'll always cherish.
"I want to thank all the Argentine fans. Thank you for always being there, for supporting us in every match, for your affection, for your unconditional support, and for making us feel at home no matter where we are in the world. Wearing my country's shirt is the greatest honor of my career, and I will continue to give everything I have every time I'm called upon to defend it."
Fernandez had been a key figure in Argentina's run to the final, playing his part in helping Scaloni's side reach a second successive World Cup showpiece. His dismissal proved a turning point, leaving Argentina to see out the closing stages of extra time a man light against a Spain side that had dominated large periods of the contest.
Both stories underline a busy few days for Chelsea, on and off the pitch, as the club balances an active pursuit of new signings with the personal fallout facing one of its senior internationals following a bruising end to the World Cup.