The 32-year-old, who arrived at the KC Stadium from Rangers last season, has featured just twice for the first team this season and is set to leave Humberside in the New Year.
Cousin spent three years with Lens from 2004 to 2007 before making the move to Ibrox, where he helped Rangers reach the UEFA Cup final.
But the Gabon-born striker managed just six goals last term and is set to be sold.
Lens are currently struggling at the wrong end of the French Ligue 1. They are hoping Cousin can recapture the form of his successful first spell in France to help lift them out of trouble.
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