The 32-year-old is currently a free agent following his release from Turkish side Besiktas last summer.
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Oxlade-Chamberlain has been training with his old side Arsenal since then in order to remain fit before finding a new club.
Speaking ahead of Celtic’s league game against Aberdeen on Wednesday, O’Neill has confirmed that his side are hoping to be Oxlade-Chamberlain’s next.
O'Neill said: "I've spoken to him, but I'm sure he has plenty of options, maybe closer to London.
"I'd be very interested in doing it. I'm surprised people haven't taken him up."