L'Equipe says Arsenal and ASSE agreed terms on Saturday over the teenage centre-half.
The Gunners will pay €30m for Saliba, including bonuses, and the defender will sign a five-year contract.
If all goes to plan, Arsenal will announce the transfer on Tuesday.
Saliba, however, won't start the season with his new club and instead be loaned back to the French club.
ASSE president Bernard Caïazzo stated yesterday: "Everything is on track with Arsenal. William will so the season with us."