Aubameyang is set to be included in OM's squad for their clash with Nantes on Sunday.
The veteran striker, despite the controversy in Gabon following the Panthers' early elimination from the Africa Cup of Nations, is available for OM.
The 36-year-old, who entered AFCON with a thigh injury, was initially called up as a reserve and then withdrawn from the final match against Ivory Coast due to physical reasons.
De Zerbi said on Friday "Against Monaco, he played the entire match with a leg problem. We sent a physiotherapist to Gabon to look after him. The controversy with the Gabonese coach is none of our business.
"If they don't want him, I'm happy to keep him with us."
De Zerbi was referring to Gabon's Ministry of Sport declaring Aubameyang had been excluded from the national team after their early AFCON exit.