Wilson, 33, is expected to leave the Premier League strugglers during the January transfer window, just six months after he joined.
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The veteran striker has fallen down the pecking order under Nuno Espirito Santo following the arrivals of Valentin Castellanos and Pablo.
According to Sky Sports, Scottish giants Celtic have made an approach to West Ham for Wilson to determine whether he would be interested in the move.
Celtic are also interested in Chelsea striker David Datro Fofana, who is currently away on loan at Turkish side Fatih Karagumruk.
