Dumas, 21, wants to leave Benfica this summer and Schalke are among a group of clubs in the running that also includes unnamed sides from France and Italy.
Tavolieri reports that the Bundesliga newcomers have already approached the player's camp directly to explore a deal.
A Belgium youth international, Dumas joined Benfica from KAA Gent in 2021 and has worked his way through the club's development structure from the Under-17s upward. The step into Benfica's first team has not materialised, and he has been left out of new head coach Marco Silva's pre-season plans, a clear signal that the Portuguese giants are prepared to let him go.
Last season he made 31 appearances for Benfica's second team across all competitions, scoring eight goals and adding two assists in 1,378 minutes of action. He operates primarily as a centre-forward but has also been used on the wing throughout his time in Lisbon.
Dumas's contract runs until 2027, meaning this summer represents Benfica's final realistic window to command any kind of fee before losing him on a free transfer 12 months later. The club's willingness to negotiate is reflected in his absence from pre-season.
Schalke head coach Miron Muslic is working to address multiple areas of his attack ahead of the club's return to the top flight. The side have identified Ben Bobzien of Mainz, who impressed on loan at Dynamo Dresden last season, as a target for the left flank. Dumas is being assessed as an option capable of covering both a wide right role and the central striking position.
Schalke's return to the Bundesliga after years in the second division has sharpened their recruitment focus, with the priority being to add goal threat and technical variety across the front line before the new season begins.