The 22-year-old has been a key player for the Ligue 1 outfit in 2021-22, contributing to five goals in 37 appearances across all competitions.
Doucoure's impressive performances in the French top flight are believed to have caught the eye of a number of European clubs including the Gunners.
However, the Daily Mirror reports that Mikel Arteta's side will face competition from Brighton & Hove Albion, Crystal Palace, Everton and Wolverhampton Wanderers to land the midfielder this summer.
The report adds that Wolves have recently joined the race for Doucoure as they view the Mali international as a potential replacement for Ruben Neves, who has been strongly linked with a move away from Molineux.
Arteta is set to be handed a significant transfer budget to bolster his squad this summer, with Doucoure, Leicester City's Youri Tielemans and Manchester City's Ilkay Gundogan believed to be among their midfield targets.