The Irons were thumped 3-0 by bottom-of-the-table Wolves at Molineux, leaving them third from bottom and four points away from safety.
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TalkSPORT says West Ham are now weighing up dismissing Nuno, who only took on the post at the end of September after the sacking of Graham Potter.
Slaven Bilic has been identified as a possible replacement. The Croatian is now in the running for a return to the bench at West Ham.
Bilic was West Ham's manager between 2015 and 2017.