The People newspaper claim that the left sided full-back is flying into Sheffield today to begin talks with the Bramall Lane club - with Manchester City and Blackburn Rovers already interested.
He is expected to sign as long as he can agree terms and prove his fitness. A free agent Nunez will be able to sign immediately.
Meanwhile PSV Eindhoven full-back Michael Ball has shown an interest with the Blades. The former Sunderland and Everton Defender is not happy with life in Holland and is looking at coming back to England in Sheffield United.
However United will first look at Nunez, if he signs for the Blades then any move for Ball will be dashed.