The 23-year-old right-back has become an important part of the squad with 134 appearances in a Blues shirt.
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Manchester City are monitoring his situation but have not submitted any official offer. The Citizens are believed to admire the French defender as a potential option for the right flank.
However, the Stamford Bridge giants are not expected to consider a sale easily as they are also strengthening defensively, with Marco Palestra expected to arrive from Atalanta.
Gusto remains under contract until 2030, giving Chelsea full control over his future amid ongoing transfer speculation.