The France international has decided against re-signing with Lens, with his current deal set to expire at the end of the 2022/23 campaign.
La Voix du Nord claims both Chelsea and Atletico Madrid have looked at signing Clauss this summer in a cut-price deal.
The 29-year-old would be available for just €10m.
Clauss, who scored five times and assisted 11 goals last season, would be brought in by Chelsea as cover for Reece James at right-back.
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