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A fee was thought to have been agreed between the two clubs for the 22-year-old Uruguay international over the weekend but Benfica have now rejected West Ham's offer.
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Sky In Italy are reporting that West Ham offered €45m (£37.43m) plus add ons, but this fell short of Benfica's valuation.
West Ham are considering an improved offer but, with so little time left in the January window, it is believed it may be difficult for a deal to be done logistically, with Nunez currently with the Uruguay squad for their World Cup qualifier against Venezuela on Tuesday.
Nunez has scored 20 goals in 25 appearances in all competitions for Benfica this season.
West Ham in talks for Ekitike
West Ham also appear to have missed out on teenage Reims striker Hugo Ekitike.
The Hammers had been in talks with the French club for the 19-year-old, who has scored eight goals in 10 Ligue 1 appearances this season.
It now appears Ekitike will be moving to Newcastle, who had a £33m bid accepted on Monday.
West Ham are also unlikely to pursue deals for Liverpool's Divock Origi and Toulouse forward Rhys Healey.
They had been looking at Toulouse forward Healey, who would be a far cheaper alternative to Nunez and Ekitike.
Healey, 27, who began his career at Cardiff and had spells with Colchester, Dundee, Newport, Torquay and MK Dons, would come in as a back-up.
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The clock is ticking. Who will be on the move before the transfer window closes at 11pm on Monday January 31?
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