Nunez is expected to move on from Benfica in the summer following an excellent season and some of the biggest clubs in Europe are chasing him.
Arsenal and Manchester United have been in contact with Benfica over signing the forward and West Ham are also keen to try their luck after failing with a bid in January.
Nunez has also been heavily linked with a move to Newcastle and it was claimed earlier this week that they tabled a bid for him as well.
But that claim has been denied and Newcastle have not put in an offer for the 22-year-old Uruguayan yet.
Nunez is still part of their shortlist but Newcastle have not made a move to sign him ahead of the summer.
Newcastle are expected to have less money to spend in the summer than they forked out in the January transfer window.
Eddie Howe claimed that the club will work under financial constraints due to the Financial Fair Play rules, but it remains to be seen if they will push the boat out if necessary.
