Arsenal’s bid falls well short of what Lyon’s asking price of around €50m for the 22-year-old.
The Gunners made their proposal on Friday and will return at the start of the week with an improved bid of €38m.
But OL president Jean-Michel Aulas will almost certainly reject that offer too.
RMC also claims that contrary to a report on Friday, Aouar has not yet agreed personal terms with Arsenal.
With an agreement between the clubs still far away, Aouar is not yet at the stage of discussing a contract with Arsenal.
Aouar is fully focused on Lyon’s game against Lorient on Sunday as the two clubs continue to negotiate his future.