Nunez joined the Riyadh-based side last summer after agreeing a €53 million move from Liverpool, which boosted the Reds' transfer spending power to bring in Hugo Ekitike and Alexander Isak.
However, the 27-year-old finds himself in a difficult position in the Middle East after scoring nine goals in his first season.
Al Hilal opted to de-register him as a league player in February, following the arrival of Karim Benzema from Al Ittihad, due to rules on foreign player limits in squads.
With Benzema now in place, Nunez could request an exit to avoid months on the sidelines, and MLS team Atlanta United are preparing an offer to bring him to the USA.
Reports from The Athletic claim a deal could be tabled next month, but they also need to free up a designated player spot, with record signing Emmanuel Latte Lath expected to move on.
With Nunez under contract until 2028, Al Hilal will demand a transfer fee to seal any exit, but they could be forced to take a 50% hit from the figure they paid to Liverpool a year ago.