The former Arsenal captain was stripped of the armband earlier this season and has been excluded from matchday squads.
Aubameyang was already facing criticism for his form this season before his expulsion from the Gunners squad and has not featured for them since last month.
Arsenal are believed to be open to a move for the striker and Newcastle United are one of the clubs linked with the player.
However, Al Nassr want to take Aubameyang on loan for the rest of the season in a deal that would also include an obligation to buy.
They have submitted an offer to the Gunners for the striker and they would be obliged to pay Arsenal €8m at the end of the loan period to take him on a permanent basis.
The Gunners outcast was away on national duty at the Africa Cup of Nations but was allowed to leave the Gabon squad after reportedly having problems with his heart.
It remains to be seen whether the Gunners striker is willing to trade the Premier League for the Saudi Arabian top flight.