Rosenior has guided the Ligue 1 outfit into European competition this season.
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The former Fulham and Brighton fullback has been linked with a return to England.
Fulham are interested in Rosenior should they lose manager Marco Silva next year, where he has been linked with Tottenham.
L'Equipe has quoted a member of Rosenior's entourage saying he is happy where he is and working with the Strasbourg 'project'.
Chelsea and Strasbourg share the same owners, BlueCo.