Bouaddi, the 18-year-old Morocco international, started on the bench for Lille's friendly at Everton on Saturday, with head coach Davide Ancelotti confirming negotiations were under way despite his club's efforts to keep the midfielder for one more season.
"Of course, there are negotiations," Ancelotti said. "There is interest from so many clubs. He is a really, really good player and I hope that he is going to stay with us!
"He is incredibly intelligent on and off the pitch, he is really mature. He is 18 years old but he looks like he is 32 when he is on the pitch.
"He's going to be one of the best midfielders in Europe for the next ten years."
Bouaddi's arrival is viewed as a way to offset the departure of Rodri, who is closing in on a move to Barcelona after the Spanish champions lodged a third proposal worth around £60m for the 30-year-old, with Manchester City understood to be considering whether to accept a compromise fee.
City are also continuing to monitor Chelsea's Enzo Fernandez despite Friday's deadline for a £120m bid passing without an offer being submitted, while Tottenham are expected to move for City's own winger Savinho as that situation develops in parallel.
Fernandez endured an awkward reception on his first home pre-season appearance for Chelsea on Saturday, introduced after the hour mark to a mixed response from Stamford Bridge, with some supporters booing while others sang his name in support — a divide that continued whenever he touched the ball in midfield.
Chelsea had set suitors an unofficial deadline of 5pm on Friday to submit a sufficient offer, wanting their squad finalised before the Premier League opener against Fulham on August 24, though it remains to be seen whether a £120m bid arriving before September 1 would test the club's resolve regardless.