Nunez, 21, was a target last summer in the weeks before Suarez left Camp Nou for Atletico Madrid. Barca held informal discussions on signing him and sending him on loan to Almeria in the Spanish second division.
However, those negotiations ended when Benfica emerged on the scene, with the Portuguese club eventually signing the Uruguay international for around €24 million.
Planning for the future continues apace at Barcelona despite last week's resignation of president Josep Maria Bartomeu and his board of directors.
Sporting director Ramon Planes is working on deals for the January transfer window and beyond, although any signings will need to be approved by the incoming president, who will be elected within the next 80 days.
ESPN revealed last week that Barca plan to make a renewed attempt this winter to sign Manchester City defender Eric Garcia, who is out of contract next summer.
Aside from Garcia, the club are in the hunt for a central forward. Before Suarez's exit, the search for his long-term successor had begun.
Inter Milan's Lautaro Martinez was the main target but the costs of signing the Argentine international have proved prohibitive.
Coach Ronald Koeman offered Lyon striker Memphis Depay as an alternative but a deal to sign the Netherlands striker collapsed on the final day of the transfer window in October.
Barca could make another move for Depay -- who's out of contract next summer -- in January, but Nunez has emerged as another option.
The Blaugrana have tracked him since his days playing for Penarol in his native Uruguay and sources say scouts were impressed by how quickly he adapted to football in Spain after joining Almeria in 2019 for €3.5 m. He scored 16 goals in 32 league games last season.
Talks took place with Almeria sporting director Joao Goncalves in the summer over a low-cost deal, although they were halted when Benfica appeared.
However, Barcelona have continued to track Nunez and have stepped up their interest following his fast start to life in Portugal, where he scored four goals and set up five more in eight appearances.
Sources at the club believe whoever is appointed as the new president will want to bring in a No.9 and the plan is to have deals lined up to facilitate his job when he takes over.