The Uruguayan's three-year stay on Merseyside came to an end last summer when Al-Hilal captured him in a deal worth up to £56.6 million.
A switch to the Saudi Pro League was supposed to resurrect his career, but after scoring just six goals in 16 league appearances, the 26-year-old's nightmare continued in the Middle East.
Karim Benzema's January arrival made his situation even worse as he was dropped from the squad altogether and has since had his contract terminated.
Incredibly, Nunez is now available to sign on a free transfer after leaving Al-Hilal, and according to TEAMtalk, Liverpool are weighing up a remarkable opportunity to bring their one-time record signing back to the club.
The Reds are joined by a host of clubs across Europe, including several in the Premier League, in showing admiration towards the Uruguayan international.
Andoni Iraola's arrival at Anfield could dictate whether he pushes to sign the livewire striker or looks elsewhere, as Nunez is set to become one of the most intriguing free agents available on the market.