The central defender, who plays for Croatia, has been impressive at the World Cup.
Gvardiol is someone that Chelsea co-owner Todd Boehly admires greatly.
Per reporter Alfredo Pedulla, Chelsea will have a meeting regarding the defender after the World Cup.
Chelsea are willing to pay up to £69 million for Gvardiol, but RB Leipzig are not in the mood to sell.
The Blues did attempt to conclude a transfer in the summer, but no agreement was found.