The 17-year-old currently plays for Universidad de Chile and made his first-team debut last November.
The centre-back has gone on to make three further appearances for the first team this season.
His agent Rodrigo Robles told Chilean newspaper La Tercera: "After Chelsea's interest, Inter Milan are now seriously interested in Lichnovsky.
"I'm in continuous contact with the Italian club and they have asked me what price he would be available for.
"When Inter bid for Edu Vargas when he was at Unviersidad de Chilie (now at Napoli), they also expressed their desire to sign Igor."