The 22-year-old forward is set to spark a major bidding war amongst several clubs in the Premier League this summer.
Manchester United have identified him as one of their top targets for the next transfer window as they look to bring in a striker for their next manager.
Arsenal have also joined the race and the north London club, while the Red Devils have been in contact with Benfica to understand the terms of a potential deal.
West Ham and Newcastle have also been keen and it has now emerged that they do retain an interest in signing him.
The Hammers had a deadline day bid for Nunez rejected during the winter transfer window and Newcastle were keen on him as well.
However, both clubs look up against it in their interest in Nunez as it is suggested that without Champions League football or an eye-watering offer then they may not be able to win the race.
Manchester United and Arsenal are pushing to secure a deal to sign him in the next transfer window.
Benfica are prepared to do business with a club who are ready to match their £67m asking price.
