Chelsea are set to make a third offer for Leicester's Wesley Fofana in the coming days.
The Blues are determined to sign a top-class center-half for manager Thomas Tuchel.
They have already secured Marc Cucurella from Brighton and Kalidou Koulibaly from Napoli.
However, the departures of Andreas Christensen and Antonio Rudiger, along with the likely exit of Marcos Alonso, mean they need to sign one more defender.
The previous record is the £80 million that took Harry Maguire to Manchester United from Leicester a few years ago.