The Chilean attacker has become a pivotal member of Arsene Wenger's team since his £31m arrival from Barcelona in 2014.
This season Sanchez has scored 10 goals, two of which came in Sunday's 3-1 victory over Bournemouth, in all competitions.
The 27-year-old's current contract at the Emirates does not expire until the summer of 2018, but he is yet to agree fresh terms over a new deal despite lengthy talks.
According to Calciomercato, Inter are keeping track of the situation and are prepared to put forward a hefty sum to lure Sanchez to San Siro.
At the weekend, Wenger stressed the importance of keeping Sanchez, who has scored 37 Premier League goals since his move to Arsenal two years ago.