The report claims that the reigning La Liga champions are considering bringing in a few experienced names over the winter transfer break to add depth.
Negredo, Jonathan Soriano and Sergio Garcia are also being considered by the La Liga giants.
January transfers will be able to register immediately unlike Turan who has spent the last few months on the sidelines due to the FIFA transfer ban that is currently in place.
The former Netherlands international joined Liverpool from Feyenoord in 2006 and scored 71 goals in 285 matches for the Reds.
The 34-year-old played in the the 2006-07 Champions League final, was runner up in the 2008-09 Premier League title race and won the 2011-12 League Cup with Liverpool.
Kuyt joined Fenerbahçe after Liverpool making a €1 million move in 2012 and winning the Turkish Super League as well as the cup.
The experienced winger returned to Feyenoord over the summer and has already racked up six goals in 9 games.