The local Diario de Almeria newspaper also states Southampton have made an offer and that Benfica have come forward.
Benfica have yet to make an official bid, but have opened talks over a potential deal and a meeting between the clubs will take place soon.
The message from Almeria to interested parties has been that Nunez can leave for €20m.
Almeria failed to secure promotion to La Liga and face losing the exciting young attacker.
Nunez, 21, scored 16 goals in 30 games in in the latest La Liga 2 season, leading to huge interest from clubs across Europe.