Free agent Jack Wilshere was knocked back by Lille last month.
Wilshere has been training with former club Arsenal after leaving Bournemouth at the end of last season.
L'Equipe says agents for the England international made contact with Lille in January to offer his services.
Wilshere was even prepared to spend time trialling with LOSC's first team squad in order to prove his fitness.
However, Lille chose to pass on the proposal.
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