The 23-year-old France international has started just three Premier League matches this season and is becoming increasingly frustrated with his lack of opportunities.
Despite Reece James' ongoing injury problems, Gusto has fallen behind young defender Josh Acheampong in the pecking order, raising doubts about his future in west London.
According to reports, Chelsea have previously placed a valuation of around 85 million euros on the defender, with Manchester City emerging as a potential destination.
Gusto is reportedly keen on a move to the Etihad Stadium, where he could reunite with former Chelsea manager Enzo Maresca.
The former Lyon defender joined Chelsea in January 2023 on a seven-and-a-half-year contract and has since made 100 appearances for the club.
With the January transfer window approaching, Gusto is expected to assess his options as he looks for more regular playing time.
Crystal Palace have parted company with manager Pierre Sage following a disappointing run of results that has left the club struggling in both domestic and European competition.
Lewis Koumas is determined to make the most of his opportunity at Liverpool after breaking into the first team under new head coach Andoni Iraola, insisting there is nowhere else he would rather be.
Thomas Tuchel has reaffirmed his commitment to England, insisting he has unfinished business with the national team and intends to remain in charge until at least Euro 2028.
Former Liverpool defender Dejan Lovren believes Mauricio Pochettino could struggle to succeed at Manchester United, warning that the club's problems run much deeper than the manager.
