TMW says Lopez has passed the required 20 appearances mark to sign permanently with the Serie A outfit.
The midfielder will now be handed terms to 2025 by Sassuolo.
Sassuolo will also pay €3-4m to OM - dependent on bonuses - to complete Lopez's transfer.
"Here I am having fun and I am playing, despite the competition. I like playing in Italy, we work a lot on tactics, we adapt very little to our opponents and we play according to our game ideas," said Lopez.
"I can say that I will stay here for the next 4 years."