The 18-year-old has already made 96 senior appearances for Lille, including 42 across last season, and is set to represent Morocco at the World Cup despite having previously played for France at youth level.
According to Sky Sports' Sacha Tavolieri, Arsenal have held positive discussions with Bouaddi's entourage, with the player reportedly receptive to the idea of working under Mikel Arteta.
The Gunners have made clear to those around the midfielder that he would be given an important role immediately, a message that is said to have resonated with the teenager.
Lille's asking price for Bouaddi sits at around €70million, a substantial fee for a player who only turned 18 in recent months but who has already established himself as a regular in Ligue 1.
Paris Saint-Germain remain in the picture and have long tracked Bouaddi's progress, with some reports suggesting the midfielder has previously expressed a preference for a move to the Parc des Princes.
Arsenal believe a key advantage lies in their relationship with Lille president Olivier Letang, whose club would reportedly rather avoid strengthening a direct domestic rival in PSG.
That dynamic, Arsenal hope, could work in their favour even if Bouaddi's personal preference initially points elsewhere, since Lille's stance on selling within France adds a layer of complexity to any PSG move.
Bouaddi extended his contract with Lille earlier this year after Arsenal's initial approach in January, though he made clear at the time that a new deal would not necessarily prevent a summer departure.
Arsenal's interest in Bouaddi comes as the club continues to weigh up midfield reinforcements more broadly, with Newcastle United's Sandro Tonali also understood to be admired by Arteta.
The Gunners are not expected to make any final decisions until after the World Cup, with Bouaddi's commitments for Morocco taking precedence over any negotiations in the short term.
For Lille, any sale would represent significant financial value from a player who only broke into their first team as a teenager, underlining the scale of the talent both Arsenal and PSG are chasing.
Further talks between the parties are expected to accelerate once the international tournament concludes, with Arsenal keen to have the framework of a deal in place before pre-season begins in earnest.