Interest in the Croatian is increasing as he continues to impress in the Bundesliga for Leipzig.
Gvardiol has made nine appearances in all competitions this season. His performances have caught the eye of Chelsea, Tottenham Hotspur and now Inter.
The two London sides were locked in a battle for the Croatian in the summer, with the duo's operations to sign the player at an advanced stage.
The Nerazzurri caught wind of the level of negotiations ensuing and retreated but appear to have recommenced their pursuit of Gvardiol.
The versatile young centre-back's price is now said to be around €60 million after Leipzig struck a contract extension with the player in September.
He is now tied to the Red Bull Arena until 2027.
Alongside Chelsea, Spurs and Inter are Bayern Munich, who are lingering and are no strangers to signing top emerging talent in the Bundesliga.
Gvardiol joined Leipzig from Croatian side Dinamo Zagreb in 2021 for €20 million and has been a mainstay in the German side since.
He has made 55 appearances, scoring two goals and contributing four assists.
Inter's interest in Gvardiol may stem from uncertainty over the future of Milan Skriniar, who continues to be linked with a move to Paris Saint-Germain.
Simone Inzaghi's side are reportedly looking to agree on a new short-term deal with Skriniar to fend off interest from the Parisians.
Chelsea need to move quick for Gvardiol
With Inter now joining the race to sign Gvardiol, Graham Potter's side will know that they need to act fast in order to secure his signature.
Kalidou Koulibaly's arrival from Napoli has failed to work out as of yet. The Senegalese defender has been dropped by Potter in his two games in charge.
European clubs are often wary of spending big in the January transfer window with the season halfway through.
However, the winter window may be an opportune time for Chelsea to secure a deal for Gvardiol and beat the likes of Inter and Spurs to his signing.
The Blues also hold a good relationship with Leipzig, having sold Timo Werner back to the Bundesliga side this past summer for €30 million.
They are also interested in signing the Red Bulls' Christopher Nkunku, with reports suggesting a pre-contract agreement has been struck between the player and the west London club.