According to Italian outlet Calciomercato, Forest have made contact with the 40-year-old Frenchman, who left Milan in May following a mass clear-out that also cost head coach Massimiliano Allegri, sporting director Igli Tare and chief executive Giorgio Furlani their jobs after the club missed out on Champions League qualification.
Moncada spent eight years at Milan, rising from chief scout to technical director and overseeing signings including Mike Maignan, Pierre Kalulu and Tijjani Reijnders, having previously built his reputation as Monaco's chief scout, where he was credited with recommending a young Kylian Mbappé.
The move comes as Forest's Marinakis-owned group, which also controls Olympiacos and Rio Ave, looks to add experienced leadership to a sporting structure that has lacked a permanent director since Gaspar's departure. It follows a summer transfer window in which Forest have been notably restrained given their resources, with free-agent midfielder Xaver Schlager and attacking midfielder Gustavo Sá the only confirmed arrivals at the City Ground, despite the club banking a substantial fee from Elliot Anderson's move to Manchester City.
Nottingham Forest's pursuit of a more high-profile addition, Sporting Lisbon centre-back Ousmane Diomande, has stalled, with Portuguese outlet Maisfutebol reporting that negotiations between the clubs have collapsed amid "a major disagreement" over terms. Schlager, an Austrian international, joined as a free agent following his exit from RB Leipzig and is reunited with head coach Oliver Glasner, with whom he previously worked at Wolfsburg.
Glasner has said Forest are targeting four further signings this summer, including another midfielder, a centre-back, a right-back and a striker, while stressing he is "not anxious" to get deals done before the new Premier League season. The head coach explained that completing transfers requires agreement between both clubs, the player and his representatives, and said Forest had already identified their targets but still had work to do to get the deals "over the line."