The Irons sit inside the Premier League bottom three and Nuno has told club chiefs his squad needs to strengthening next month to stay up.
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The Mirror says FC Utrecht wingback Souffian El Karouani is being prioritised by West Ham.
El Karouani can leave Utrecht in January for a price starting at £3m, though Fenerbahce are also interested.
West Ham are also seeking a new centre-forward addition with Niclas Fullkrug now in Italy to sign with AC Milan on-loan when the market reopens on January 1.