While highly rated at the Emirates, the 19-year-old is not part of Arsene Wenger's plans for the new campaign and the Gunners manager is said to be keen to send him out on loan to gain experience.
Nice have also been linked with Reine-Adelaide, but former Leicester City manager Claudio Ranieri's Nantes are the favourites to secure his signature, according to L'Equipe.
The midfielder made six first-team appearances for the London club last term across the EFL Cup and FA Cup. The last of those games came in February and he was excluded from the team's pre-season preparations due to injury.
Wenger has admitted that he needs to cull his roster before he looks to make further additions.
Reine-Adelaide is contracted at the Emirates until 2019.