The bid and rejection were confirmed by multiple transfer journalists, with Lille making clear they regard the Arsenal offer as significantly below their asking price for a player who has attracted interest from Chelsea, Liverpool, Real Madrid and Paris Saint-Germain in addition to the Gunners.
Bouaddi, a France youth international of Moroccan descent, broke into Lille's first team this season and demonstrated a technical maturity and creative intelligence that led to widespread comparisons with some of the finest midfielders to have come through the French system.
He is under contract at Lille beyond the 2026-27 season, giving the club full negotiating leverage.
Arsenal sporting director Andrea Berta will need to decide whether to increase the offer to meet Lille's valuation or redirect the budget toward other midfield targets.
The competition from other elite clubs means delaying a decision risks losing the player entirely if a rival meets the asking price first.