According to the BBC, the 23-year-old France international is increasingly frustrated by his lack of opportunities, having started just three Premier League matches this season.
Despite Reece James' injury struggles, Gusto has lost his place to youngster Josh Acheampong.
The Blues were previously willing to sanction his departure for approximately €85 million, with Manchester City emerging as a potential destination.
The former Lyon defender reportedly expressed interest in joining the Citizens, where he could reunite with former Chelsea manager Enzo Maresca.
Gusto, who joined the Stamford Bridge giants in January 2023 on a seven-and-a-half-year contract, has made 100 appearances for the London club and will assess his options ahead of January.