Zappacosta only joined Chelsea from Torino last summer, but he struggled to earn a regular place in Antonio Conte's starting XI and was limited to just 12 Premier League starts during the 2017-18 campaign.
Conte's own future at Stamford Bridge remains uncertain, and Tuttosport reports that the manager's position is also raising doubts over Zappacosta's long-term future at the club.
Inter Milan are reportedly interested in the Italy international and would hope to initially take him to San Siro on loan, with an option to buy at the end of the deal.
The 26-year-old would likely command a high transfer fee should he join permanently this summer, having only served a year of his four-year contract following his €28m (£24.7m) switch to Chelsea.
The Blues would hope to recoup the vast majority of that fee, although that price tag is likely to drop if it is preceded by a one-year loan spell.