The Italian newspaper claims there is a possibility that the Croatian international will be sold at the end of the season as the Nerazzurri look for ways to balance the books.
Brozovic only signed a €6.5m a year (£110,000 a week) contract in March last year, but the interest from the Blues and other teams may tempt Inter into selling him this summer.
Ironically, it could be the case that Brozovic is being eyed as a potential replacement for his international teammate Mateo Kovacic.
The Croatian will have a year left on his current deal at Stamford Bridge come June and there is increasing speculation that he will leave Chelsea.
Brozovic is a couple of years older than Kovacic at 30 years of age, so it is questionable whether he would be much of an upgrade.