Skriniar played a crucial part in helping the Italian giants lift the Serie A title in the season before last and his form continued in the same vein this past campaign.
The centre-back made 48 appearances in all competitions for Inter in the past season and added to his trophy collection with the Coppa Italia and SuperCoppa Italia.
His defensive displays have seen him become a target for the Blues, who are losing Antonio Rudiger and Andreas Christensen in the summer, leaving places to fill in the centre-back area.
The Blues have competition on their hands though as Ligue 1 champions Paris-Saint Germain have added him to their transfer list, according to French daily Le Parisien.
Luis Campos, director of football at the French club, travelled to Milan earlier in the week to start talks with the Serie A side.
Skriniar has regularly been linked with an exit from Inter in recent seasons, but has continued to stay at the San Siro.
Inter signed the 27-year-old defender from fellow Italian side Sampdoria in 2017.
