The 21-year-old could become new boss Mikel Arteta’s first permanent signing since taking over the reins from former manager Unai Emery in December.
The Gunners completed loan deals for centre-back Pablo Mari from Flamengo and Portuguese right-back Cedric Soares from Southampton in the January transfer window.
According to Jeunes Footeux, central midfielder Gueye could join in the summer for as little as £5million.
This wouldn’t be Arsenal’s first foray into the French second division, having picked up Matteo Guendouzi from FC Lorient in 2018.
The 20-year-old box-to-box midfielder has hit the ground running for the north London club, making 21 league appearances so far this season.