The 18-year-old had a breakout World Cup this summer, featuring in five of their six game before being eliminated by France in the quarter finals.
According to reports from Sky Sport, Man City have now moved ahead of Premier League rivals Arsenal in the race to sign him.
Arsenal were previously considered favourites to sign Bouaddi, but they have now turned their attention to Newcastle captain Bruno Guimaraes.
Negotiations between sporting director Hugo Viana and Lille president Olivier Letang are described as almost constant, with the two executives having regular phone calls.
Lille have maintained a firm stance on their financial demands and continue to hold out for a symbolic €100 million fee.
City are hoping to get a deal done for closer to €90m.