The former Dagenham & Redbridge defender suggested that he was going to bet money on the German international joining the Gunners on deadline day by writing on Twitter: "Lovely bit of 14-1 Mesut."
Ozil, who is currently on international duty, eventually completed his switch from Real Madrid to the Emirates Stadium for a club-record £42.5m fee.
"We take this very seriously," London 24 quotes an Arsenal spokesman as saying. "All Arsenal employees and workers are well aware of their responsibilities in this respect and we are looking into this as a matter of urgency."
If found guilty by the club, Arber could be in breach of the Football Association's betting rules.