Thomas Tuchel wants centre-backs adding to his squad at Stamford Bridge and the club recently lost out on signing Jules Kounde, who opted for Barcelona.
Chelsea are looking at a number of other options and are now showing keen interest in Croatia international Gvardiol.
Tuchel even called Gvardiol last week to register his interest, according to German broadcaster Sport1, and are attempting to sign him.
However, RB Leipzig have been clear that they do wish to let the player depart this summer and have slapped a not for sale sign on him.
RB Leipzig are battling to keep hold of their top performers and saw off interest in Christopher Nkunku earlier this summer.
Now they are fighting to keep Gvardiol out of Chelsea’s clutches in the ongoing transfer window.
It remains to be seen if the Bundesliga club will be able to stand firm if Chelsea put in a big bid for the Croatian soon, with the window open until 1st September.
