The France international remains on the transfer-list at Chelsea after being urged to find himself a new club last summer.
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Foot Mercato says BVB coach Niko Kovac regards Disasi highly and would like to bring him to Germany in January. The pair worked together at AS Monaco.
On Saturday Disasi made his first appearance for Chelsea's U21s team in their 4-1 win against Reading.
Disasi, who is under contract until 2029, joined Chelsea from Monaco in 2023 for €45m.